Physics-
General
Easy
Question
Three identical plane mirrors AB, BC, AC are arranged as shown in the figure. Find the total number of images of a point object ' S ' formed by the three mirrors. ( S is at the centre of the system)
![](data:image/png;base64,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)
- 18
- 12
- 5
- 15
The correct answer is: 12
Related Questions to study
physics-
A transparent solid sphere of radius 2 cm and density
floats in a transparent liquid of density
kept in a beaker. The bottom of the beaker is spherical in shape with its radius of anvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an abject is placed at a distance of 10 cm directly above the centre of the sphere its final image coincide with it. If ' h ' is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is
and that of the liquid is
.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/556620/1/1047017/Picture109.png)
The value of
is (nearly equal to)
A transparent solid sphere of radius 2 cm and density
floats in a transparent liquid of density
kept in a beaker. The bottom of the beaker is spherical in shape with its radius of anvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an abject is placed at a distance of 10 cm directly above the centre of the sphere its final image coincide with it. If ' h ' is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is
and that of the liquid is
.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/556620/1/1047017/Picture109.png)
The value of
is (nearly equal to)
physics-General
physics-
A transparent solid sphere of radius 2 cm and density
floats in a transparent liquid of density
kept in a beaker. The bottom of the beaker is spherical in shape with its radius of anvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an abject is placed at a distance of 10 cm directly above the centre of the sphere its final image coincide with it. If ' h ' is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is
and that of the liquid is
.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/556613/1/1047015/Picture31.png)
The image formed by the top spherical portion of sphere is (as measured from top of spherical ball)
A transparent solid sphere of radius 2 cm and density
floats in a transparent liquid of density
kept in a beaker. The bottom of the beaker is spherical in shape with its radius of anvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an abject is placed at a distance of 10 cm directly above the centre of the sphere its final image coincide with it. If ' h ' is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is
and that of the liquid is
.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/556613/1/1047015/Picture31.png)
The image formed by the top spherical portion of sphere is (as measured from top of spherical ball)
physics-General
physics-
A ray of light is incident normally on one face of
prism of refractive index 5/3 immersed in water of refractive index
as shown in figure.
![](data:image/png;base64,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)
A ray of light is incident normally on one face of
prism of refractive index 5/3 immersed in water of refractive index
as shown in figure.
![](data:image/png;base64,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)
physics-General
physics-
Two identical thin isosceles prisms of prism angle each A and refractive index
are placed with their bases touching each other. This system acts as a converging lens. What is the focal length of this system for parallel rays at a distance h from the base of the prism ?
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)
Two identical thin isosceles prisms of prism angle each A and refractive index
are placed with their bases touching each other. This system acts as a converging lens. What is the focal length of this system for parallel rays at a distance h from the base of the prism ?
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)
physics-General
physics-
In the given figure, there are two thin lenses of same focal length
arranged with their principal axes inclined at angle
. The separation between the optical centers of the lenses is 2f. A point object lies on the principal axis of the convex lens at a large distance to the left of the convex lens. Find the co-ordinates of the final image formed by the system of lenses taking 'O' as the origin of co-ordinate axes.
![](data:image/png;base64,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)
In the given figure, there are two thin lenses of same focal length
arranged with their principal axes inclined at angle
. The separation between the optical centers of the lenses is 2f. A point object lies on the principal axis of the convex lens at a large distance to the left of the convex lens. Find the co-ordinates of the final image formed by the system of lenses taking 'O' as the origin of co-ordinate axes.
![](data:image/png;base64,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)
physics-General
physics-
An equiconvex lens
of focal length 20 cm is cut into two equal parts and one part
is silvered. Another concavo-convex lens
(radii 10 cm and 20 cm, μ=1.5 ) is placed with its principle axis 2 mm above the principle axis of
A point object ' O ' is placed at a distance of 80 cm from the lens on its principal axis as shown in figure. Find the position of final image.
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+fPq30SiyJ0IgP4XnP4sWLA2r48FxRPdOjaZUOBvS0pMdlcLx7905kVOBrMD2UxHqR4iMJEjobDB06NGBFGlxJZFPRuXNn8f403XA3JrEsQis+KnSpV81wdCphyh3ubPnfTLMU0jU2cuRIMZa5AaU51rqR4iMJFppHChQoIG542uuDs8WbAppV/vrrL/H+0r5vefys+BC6ZKtOJXSrpghRTDZv3qyM0ObBgwfIkiWLeF5IYyWWjxQfSYjQ442xNwwCZWlsc7N7924xSdFz6tixY0qvxBIIi/gQ7lqGDBkivNsYlFq3bl1xNhQcDFzle1WsWDHERKPctTMTdkju3ZKIQ4qPJERY5vjff/8VNz4Pjs0NJ5I+ffqI96f5T2bAthzCKj6E4+fMmSPOFenW36lTpyBz+126dCngvCi4Et0q9vb2Il9hly5dzB4sLQkdUnwkoYKlj3nwz4kiuEqVpoLmP7Vgmblzz0mC5lfER4UVbpnHja/DYFRjsaBrtnr2x8S3IeX+o2l44sSJYjxjhqRHnGUixUcSKnhDN2/ePGACiAh4OE3vN050EWH+k/xIeIgPOXz4sPB442s1atQokAAxODVevHjC9BuarBfPnj0TJlpeK/SIM3eYgCR0SPGRhBqWP2Dmg6RJk4osCOaG2Q8aNGggJqgBAwaY3flB8iPhJT6EaXlUhwKaeen5xl2P+pv36tUrVOmeGJfG8TS7SQ9Jy0WKj+SnUBOPcnL48uWL0ms+uELmCpiZt2Vt/4gnPMWHcFGj1ghikcMVK1aIf6dLly5U5t5bt26JBRKdGDZu3Kj0SiwRKT6Sn+Lu3bvi7Ie7H9ZtMTf0XmLNH05INP/J3U/EEt7iQ2haUwNJKUQ865sxY4byaPA0adJEPI8xQ15eXkqvxBKR4iP5KTjZq55n7dq1M2vWaxUmkqRNn+7XEWH+k3zHFOJDLly4IMo08LW5A6L3WkjwbEj1nJPXheUjxUfy07DyKA+AM2TIEGEZhVW7Ple4MpYj4jCV+BCeATG2jCY0BhgH9/pcFNWpU0d8Frkjtg6k+Eh+Gsb9qJ5vw4cPV3rNCwuIcWLiKnffvn1Kr8TcmFJ8CDMZcDdDzzVmWg8KjuO1wPOeGzduKL0SS0aKjyRM8LwnRowYIg0+0+FHBP379xcTH11z5Uo3YjC1+JAlS5aIa40CxHILxtALslq1auJzDBw4MFSu1ab6rJLQI8VHEiaYXZgmL97wnBwiYvLnCpfnPunTpxdu4BLzYw7xIQwspgAlS5ZMmOMMUT3iaAYOzUKI1w1d9c1dp0oSGCk+kjBD0WFuLubaioiM14YxIMy+LTE/5hIfeq6p53zcbT969Ej0Mx/cP//8I/pZEyikRRDPB1WPOL6eJOKQ4iMJM/fv3xcZp2lrp3dSREDzHycSmUYlYjCX+BBmPVAr3NavXx8fP34MKCzHyqYvXrxQRgYN00RxPL0lWa9KEnFI8ZGEGa4imbiRNzNrskSE1xl3XIULFxaFyLgTk5gXc4oPoclMzYLAgOcaNWqIf7NQXUjw+ixXrpwYHxEJciWBkeIj+SWYFJKVTnPlyhUhpjceLi9atEhMKEzL/+HDB+URiTkwt/iQHTt2CFd/vi8Djln91NHRUXk0aOgRx+cwWwJrA0kiFik+kl/izZs3oiQyb2rjg2BzwSSjjISPGzeuCDSUmI+IEB8ybtw48b48/7lz547SGzRubm5ih8znsBqqJOKR4iP5ZZjwkTd1x44dIySDMCe9nj17is8wadIk6XZtRiJKfD5//hxQY4oOBCHlGWR2a46lyY4LJknEI8VH8suwuBcTfbImCw+BI4INGzaIOJBKlSoJN3CJeYgo8SE3b94UJjS+/7x584JcdNAkxx0Sxy1cuFDplUQ0UnwkvwxXoXny5BFu1xFV5poxG3/88Qfix48v0v9IzENEig9ZtmyZiPViHrigsl6PHTtWfEZ6RAa1OGLCXCcnJ+W/JOZAio8kXFAzTTPCPCJgHEirVq0CVreWZnrzcXuFaxcu4f5rD6XHNPj6foOvGb96RIsPFz5qqqdatWqJ/zaE50FqiYZt27YpvYGh6DBWqHr16iJtk8Q8SPGRhAvr1q0TOx8e6kZEpmsyd+5cMclwQjSehCIUvy+4trQtsmfIhIq9VuJJuP95vsHx6k5M6N4Lsw/ehVsUEh/CXQu9Lfk5DBcedK0ePHiw6KdLNtPwaKE6L7BUSESlioqKRIz4+HzErWObMGfCMPTt0R3de/XHiClLsN/mKUy7LpSYipcvX4oaP7yBIyptCTNs//7778L0pkbAWwR+3ri7rityZciK6oM2wiHcfDJ88Obmfkzt2xTFsiXXT6BxUGf2OZhTdi1BfAjjfGh+4xmQuntRS2/QCzKo2lMMlKa5lt+BGRIk5sPM4uOLF2eWoUPVYihSvhEGTV2MDVu3YdOaRRjTuxlK5s2D8m3G4ehjN2W8xFrgapPR5zz05w4kIuDkR9MJJ5I1a9YovZaB7xcXODx7gXefwrHAmY8XnOwf4uaZ9eheNo3+eydC0yU20F7fmwZLER96u6nJRfv27St2OWrVXZqEmYpJC6Zl4ph8+fJJLzgzY0bx8cS1tf1QIE1iZK08APvuOcP9q7oE9IO3+0fc2TcR5TPER/L/tcQKu/d6qZJYE3Rz5o3ctGlTpcf8jBo1Spj/eP4TkZOhWdALvr+B6QN2Di+PmPqdT6MoKj6EMV5MPJoyZUpRfoELIf53UIXlmIw2a9as4vNb2mIlKmAm8fGFw8HRKJxCh+gZamDt/aBWf164saYrfoumQ8p/umPfU0+lX2INnDp1StzIxYoVCzHuwlTs3LlT1HRhzjnWHYoaOGPP2GqIqxefhlFYfIi628mRIwdKliwZZL0p7oTUkhyVK1eOkOwcUR3ziI/LeQwUZoHoKD7oCIKblr69scGw0gn1YxOi/LDteKO9W5ZYIEz8yLQnmTNnxrVr15Re88IDYwYS0v4fmkST2nyD483T2LlhDVavXIFV67fj5NXn+r27AX4++PzuBe5cvYBjBw7juqO78oAeXxfcOrETO45exVvlST4fn+PSsSM4fflJ4NeBOx5cOIBtW7dh+/YdOHDiNM5cuIGXzj9jeqb4VEc8IT6XorT4PH36VJz78ToMLqbn4sWLYofE88Fdu3YpvRJzYhbxsd/cB7nj66CL+QeGHg9hheH7BntGVkBs/QUd48822H3P4KaWWDRMYVKiRAlx469fv17pNS+cAIsWLSomxKAOmYPF9yMuLhuImmXKolH3YRg6uB/qFc2OdFlLoMcKW7gpnmq+7+5gw7g2+OePNIiuX1Tl6bgOr/mA92vsHVMH6fTvr4tRCgtOXcH5Q6vQ998iSBc/MQq1XoTvubc/wXbVcLRr2xOjJk/BtKlTMLhNRWTKXg3zztkrY0KDFB9D1EzXRYoU0YzdcXd3R/v27cUYmogtyjMyCmEG8fmEbYMqITFvxhQ1sNY+JFOIJ2zXdEZGcfPmwchDD/XrUIk1QNfW3r17i5uaNfcjipYtW4rPMH78eKUn9LhdX4ASCXRIVnwQrit9XhenoWhS/fWYuT1OffTP3O37+TVunNmHTctHoEI2/U49WQWsu/8GN7aMRMO6zdCtWzs0aTsOR+/cx+VTOzGq1u/6zxQbxbus9hcpPT4P16Le33+h05bvSTE9H61B40qNMfvoM6UnNEjxMYQmNAY9M9P5rFmzlN7vnD59WuyMU6dOHWH5CCVmEZ+HmNeqoH51qEPMLC2wzymkswBf3Nn1H/JE09/surRot9oOcu9jPaxdu1ZMRo0bN46wQM/p06eLw2bm/vpZPpwZiexxE6Fwxw3fXZY/7EebfEkRLW5FrH314/V7dkw1pE6YAKV6TMWYgZNwxN4Nft888cnNM8Bpxn5NE8TUxUXxzisDxMfj4EBkS5YUJQfswruAahTeOLt1G05cf/YTDjdSfIxhpmt+Lu7EDc2v3PWoHpEdOnQI0gtOYnrMID73MKt5PvFjx8rWEvtDFB/g/t5RKBiT4pMKLZfbQDpeWw/0IOJvXbx48VCluTcFTPHD2A7Gb/zshOjr4YQH16/h0RtXeLq+xwObA5g/uD5yJI6FGEmrYrXDj04wXhcmoXDKaIidpRYWXtJK3+KNh6tbII4uXiDx8X28HvVyxIMueiLkr90HK4/dwUf9XOjn6wtfXx/Fky00SPExhm7TvAbp+UgznMqePXvE5+W5kI2NjdIriQjMID6vsKLrP/obT4doaeth86uQPNh8cXvnYPytH6/TZUe/nbf1t67EWuCBb6pUqYQLa0TlWOPEkyZNGuFmy+j3n8cN944uQe9WTdCy2xis3zoV9XKnRKyElbDqpcb1++Uk2v6RDEmzNcMhzW06xac54hqJD/tvbR2JSjkTIxqv9+hJkKd6T6w9b4+fm8al+GixatWqQAsh7sQLFSok+hgLJIlYzCA+33B+emOkoxktbiFMtvuk9AeFGy4ub4c0vBlT1cAKO5nsz5rgxM+DXhaY279/v9JrfgoUKCB2P7t371Z6Qse3z/exrHdV/JW3CibuvIFP3j7Ap8PoWDAlosevoCk+Pi93o03eRIiRojCm2Gjt7IMSH3/cn5/F/IFNUej3JGJi1KX+B6N2P4BXqO1uUny0oOCULVtWfD7G8bDSLf/NhdHjx4+VUYHhuSXPgQ4fPixMdBLTYQbx0d9cVxeg8u8x9T98ItSdc1PpDQIfB2zqW1BcJBkbTcediMnQLwkj9BzieQ9/v5UrVyq95odJJnmoHJryyt/xge2s2kgUKzlqTjIwyXgcR5f/6cUnnl58HI1i1L69xr5Z4zGoST7ETpIRDWffUB4wRFt8vtpfxw3H7w44zrf2YkSDAkimX6glqTQedz6E1tVGik9QsMptjBgxUL58+QAvyAkTJiiP/ghFiY4I3DkzPY/EdJhFfPTrYWzvV1p/8+mQvNRgXA1mQeH1aBeaZtKv/pIXxoTD9tLkZmUwqeiQIUPETc6MBxEFC9vR3j9mzBilJzR8xpKGv0EXIykaGIiI241FqPp7HERLVAXrHL7C74uHXqbIN9zbMRWjFhzE3RMTkDdhEuRtsVI4yLy6fwO3H75SnAa+4tGaFnpx0ItPl1X6u8Ef94Oj0Hr0TjgYaszLPWiTJw50uXvj8psAL4QQcMbecRSf2Gi01LxnpJYuPs+ePRO7YDqg8FqgGAUVUMpr97///hPfh6miGLcmMR1mEh/9mvLVGQytnEn/wyZBrQnHoLmhcbuHuc1z6yeNzGg08yTeW961LAkFvMF5A7PCaUR5vI0YMUJ8hu7duys9ocEbJ0aUQSz985LkrIbhc5Zg7qQxGNyrPvKkTqgXpbSo0qUvOrVqhc7jlmDTmjno13ciTrz4DB/Pc2ibOTZS5GuCBTt3Y97UuThy30lxGvDF3YV1xefJ32ohVN8rzyP/4e9s+dBx4Wm9fPjz9e4q1MmVBv8M2oP3oU4D54Tt//mbl6rPumBW71BLFx+iLoa4IAkOng8mSpRIFEbcunWr0isxFWYTH+JhfxYTmxdCsiSZUKf/fJx+8A7ePj76G9cJt46uQr86BfBbxoLouvgMnMIx/6LEvOzdu1fc7A0bNoywAD5Gt/MzNGjQQOkJHV9ensDwuvmRQP/c6Clyo073qTh87SIWdiqFFAmSo0itNmhYlGczsZGpZFusOO/gvzv3+4DtPfNBFzMeslfqgY02jv4Z2n1e4viaKWhaKKX4PPEzFkbbaTtw/70PfM9NRrn82ZAxZxHUaNwePXr2Qpc2bdBz4gbccQ7NDeCNd7cOYe7ILiifM7F4/WR5aqH/5MU48dA8EmQN4nPhwgWR7ZrZDILLuK7Wg6pbt26EpYeKSphVfIivqyMu7piNni3+Rc2qlVCxYgVUrFwZ1Wo3QqdB07Hv+qtg0+9ILJ8zZ86Im7hcuXIR5m7NHG/8DDxw/lm8Pjji4d1buHXnIV5/9reJff3ogIcPHsPx3UfY227FzOnzsdvOAYYS4fr8PFbOX4hddi+/X8N+nnB68Ri3b9wQhc1u3ryB249ewdVbvyfy/ACHl/Z4dPcmrl65ihs3buL2A3u4hNbapt9ReX1+iyf3buOm8vo3rt/E3YfP4OQW6hf5JaxBfGhO40KInzOo4Odz586JzBzBJSKVhC9mFx8Vb3cXvHvlgBf29rB/4YDXTh/haZ77RWJieFDLG5lurUF5FZkarnY52fzvf/+Tq1gTYg3iQ7Zv3y68H/k5jUtpU5zUcgwsvyAxDxEmPpLIyw39Kjxt2rTImTNnhBWWY0ExOhwwu7WDw/dsapLwxVrEh27TefPmFZ91x44dSq8/LK+dMGFCseuJqOs1KmJR4sMDP14YMvLYulGrQ9JdNaICTZ2dncXuixmu5YRiOqxFfIhaQqFZs2ZKj39ogBoLRMcEifmwGPFhWha6RPIiyJgxI9atW6c8IrE2eEOzlgrNHNevq+k5zQ9LerO8A7MuSEwD8+fxnqXIWzosrU6nAwql6gizbNkysUhhIlJmZZeYj3AVnxkzZohU5WFpNI/wIlYbV830PtEaK5tlN6ap/+2338TvSFu61hhTtxYtWiBOnDgi00KdOnU0x8j2640LRf7ONFu1bdtWc4ylNM4nXBAx23XVqlVFn1rJlMXn2rVr98NzrKlRXK2JcBWfggX9MxPIJptssslm3nbixAllJrYOwlV86B/PAK2wNm5/eUjMtChaj8tmPY2rS94QNHNoPW7qxlLajGpn46pca4xsv97U35l/Z63HLa3xuuAco07Y/LcaWGrc6ICgfj/+v9YY/5YUyZKnQPIk8RFDvG4MxEucHClSJENSzfGmaZcuXVJmYusgXMWHdlQe9Ia1HTlyBKNHjxbnPUxQqTVGNstvz58/R/369cVNy7oqWmNM3XjOQ9MtzX+HDh3SHCPbr7fKlSuL35nmN2u4Z5luh+eRqvjUqFFDlF43Hkd3bMarZcuWTYzjkYLxGLV9cHHFJ6f72DisNtKK102FKv1X4vY7F7h++qj5HFM0S3f4MMZiHA4kkQcW6FKjxX82q3R44eHhIRJEclKMSKeHyE7t2rXF70zHDmth5MiR4jNzt0A366AYOHCgGMcs7caxQYFxx/nFXZArHoUnmn95jNhZ0XrWcYSUwz8qI8VHEu64urqKA3/euMHd3KaEkwW93Sg+V65cUXol4Y01uVqrsFwCP3OxYsVgb2+v9Abm/PnzSJ8+PWLGjBl8njfv1zgwtRkyx9Ahcbpc+DtTIiTI+Bf++j2F/j1+Q73R22H/PXG5xAApPpJwh+ZXerzxBjcO6DMXHz58EJ5unBQZ9CoxDdYoPqpJljvjs2fPKr3f4fVLzz1+r3r16onFlCYud7F2UFWk1o9L+r/O2LhrJ0ZVTYL45QZh+95dGFA2jf41EqNUt4W45hQxCXYtGSk+knDHxcUFjRo1Ejfvrl27lF7zwhUtD8EZ7MozKIlpsEbxoZg0b95cfG7DEtsqLCbHhQt3zvy3Ft4vTmNS8/yIr3+N1CW7YNv9z4DHTYwuExcxig2EjQvg+ewwBlXJrH+fmPij3ggceSS3QIZI8ZGEO05OTgGT0oEDB5Re88LMCnx/uv/L4EHTYY3iQ9Ss5506dQqU+487Zjoh8LHOnTvDy8sou7ifH97abUS3Mr8Jz7bcDUfj+DPl+np3CSP04hOzWD+cVjI6eb2+iBltiiCmfmyqIm2x6pwDvslNkECKjyTcYS610qVLiwqSERV7wBLenEBKlSql9EhMgbWKD69LulmXKFEi0LmPmg2dDhRarsvfHC9idLU0iBM9HeqP3IgHnwwqAb79UXyIn/sz7J7UEllixUbysoP0YhVY0Hy9PuPVoxs4f+Ycrj10gEsUybAsxUcS7tCmnj9/fhFTwYPbiGD58uViEqE3lsR0WKv43Lt3T2Q1YCyPmkuSu558+fKJ7zN48GDR9wM+b3F261Is33YJH/3L1H4nCPHx5zOu7lmNxRtPwPHr963Pxzu70b9mXiSPFxexY0ZHjNjJkLd6D6yzeaVUy428SPGRhDu8sbNnzy68hSLK04x1+jmJdOjQQemRmAJrFR96QzIonp9dDQdYsGCB+G+m+mLsz08TrPj8iPfLo+hZKivS/1kcdZq0QovGNVAgfXzxGRLkqIOlV4Jz77Z+pPhIwh3G1dCTiIf9LHAWEfTu3VvcxEOHDlV6JKbAWsWHcHfDzz5z5kxxTsnvQCeVqVOnKiN+kp8RH98vOD+9OSq3nYyzLzyVTuDNpZVo+Ber0kbDX82X4VUkPh+S4iMJd2grZ4okBudFVEbpxo0bixiNWbNmKT0SU2DN4rN06VLx2ZmUk84F/DeLD9L8FiZ+Qnx8vzzFmvFTccrxx7/Z/aUtkCqGDglztcUh81RDjxCk+EjCHaZJ4o3Mien9+/dKr3lhACEzGG/atEnpkZgCaxYfulHzzIcpdLhQYful6+VnxOfbJ7x0+ACtjY3frTkonDgmEuvF50gk9s6W4iMJd9avXy8mJJ63+PiY/9iU9vx06dIhadKkuHr1qtIrMQXWLD48m1RriLHRxfoH1+qf4SfPfILi67UZKJQiAbLWnQvxMn6++Ob6Cra7F6J/m0YYt+cFvrg64vCCgWhYpSzKVmuBcZts/VP5+L7H+Q0T0b5eJZQuWx3dpu/E04AYWf3reLzHjcPL0L9ZO4xedwGffD/i7MrRaFG9LEpXboRhS4/hjXCkcMHV3XPRvWEVlCpdFR1GrcGtcD6CkuIjCXdoM+fNHFHnLfSwYzZtussyx5vEdFiz+NC8VqVKFfH5hw0bFjYnA0PCSXyeLG+JDKmyostm/+BoT4er2DC2BYpm4VmQDmUHr8WiYV3RuEkT1C2XD0mj6RAjcRGM2HoYG6d2R82qNVCnWilkT6YX1Vhp0GTWKXzgFsvtLjZP6IXKuZPoXycBKvQYi1lzh6J1/X9Rt2oRpI6uH58oP3rN34m9ywajXqWKekGuiNwpo0MXLSWqDNqG8EzUIMVHEq5w5dizZ09xk/AgNyJYvHixiDHixCIxLdYsPkTNdBAuOQjDQ3y+PcLk2n/izxpjcVtZN/n5eMH14z3MaVkIcfSfNVutIdhw9jE+unrgi6cDtgythiT6/sR5amLwkmN44vwZHp6euL9zNArH0iF6scGwcdRvZ3y94fbxMXb8V0r/naMhc9l2WHbmDpw+ucHzywecm/OveJ34v5dE7wU7cfuVC9z1r/P60nQUjatDvL8aY/tL/88UHkjxkYQrqgsrA/giqhR6t27dxIQyaNAgpUdiKqxdfFSvyClTpsDP7xeX9b8sPn54trkPihaqgTkXnJQ+la/YN7QKkuk/a5XpN/T/9R37HcOQP54OiarPwhPDNHSP9qLd3/rdTIbmOPRAzfLhicvLGiO2LjYqDt8Ow3f5cGs2CutfP1XZvjhhaGJzs0PP3NEQLUNpzLENv62PFB9JuOLo6CjiJHiQG1ReLFNTrlw5MaFs3LhR6ZGYCmsXn8mTJ4vP36VLl0BpdgzZvn07hg8fjtu3bys9QfCL4uP5bAc6VymP7kvs8KOx2Av7hlVBcv1nrTH7biDxcdw7BkUS65Ck9lw8MxSfJ/vRuZBefNI2wu67anEHN9gub4J4ujioOmY3DN2B3t9djNLRdEhTYQBOG4jPt0/XMbBgdOjS/YPp58PvDFeKjyRcuXv3rnCzzps3rzjQNTfv3r1Drly5xM4romKMohLWLj5r1qwR12ulSpXw6dOP1XfYp2Y90EpCGohfER+n65jVqS5aj9+L15o+D9/Fp/qsO/BWeomDXnwKU3xqzcHTz0onebwPnQpGC1J8qozeFWjn8/7OIpSOrhef8v1xysDb/NunaxhQwF98ZkjxkVgqBw8eFDcqPYeCWkmaklOnTiFVqlSigqnWZCIJX6xdfI4dOyYConPmzCkCTY2ZPn26KKFN55UQY9bCKj6uD7B+aEu0GLzWwDPNGCk+EkmQ0GY+bdq0ADNGREDbPZ0NeO7EiqoS02Lt4nP58mUhLClSpBBlwA1hKQ7u4Pn95syZo/QGQ1jEx+sl9k7vjjYDV+CBcUCpjxecHR3gLOZ7L+wPEJ+7Py0+ewzFZ0VTKT6SyAU93Vq2bCluVoqQuaH4/fvvv+L9Fy1a9OsHyJIQsXbxoWmYZlouWJiN3RC13DazHtCcq8LrSvPKCoX4BLomv77CniltUb3JcBx8+BafXV2E+/cHZ2c4v76D3QvGYtDYTXAUg31xaFhV4XBQfc590aPy9uB4IT6Jay+Ao6HJzv4wulJ80jTGvkdqCh8vXF3ZFHF0sVF1zD64KL3E9dEyceaTuuJAnDcUwi93MEic+ZTELP8crOGCFB9JuMEKkLlz5xa18SOiiJw6kTBSPcTDYUm4YO3iQ8FRA00fP36s9AI3b94MODvcsGGD0qsXjy/PsWfeCIydsxfPjL0CghMfr1c4vGgChs/chidf/ODr+gQbh1QWrs187zjx4iCWkmUhZgz9RM/++NnRY9Mz+H51x9vnZzCiehbRn6X5Ytx4/gafPbzw6fVj7B7bECk5Pmc77LJ9ivefv+DLR0fc2j4BZZLz9f/G0C0X8PL9B/3r2GJxh9zidTLXG4Wjj17hs5cnXN4+x5k1nfEbXydzNcw69hhvXb/A3eUtHl5YjKpJ+Trp0WrWOf3ruIVLxm0pPpJwg0F6TMxI+/mTJ0+UXvOxevVqcXhcsmTJsOfnkvwU1i4+rLpbvHhx8R1ogiPMyjFw4EDRV716dTjrdyIqPq/sMKleBsTQxUWJ9tNx1t6gUGEQ4vPlzWUs6lERiXXRkKb6KFx09IX3nXXoXLcCypWvgArly6FsmTIoY9RqtRmPC3x5lyc4uGggmtWpLBwjqtRpg3HL9+Dm83e4ums6uresh4r6/kqV66HrmIU4cfMVHG03Y0TPlqhRUd9fsTKa9hqNtScv4uDSiejcwP91KtVthUFTtuLmWwdc3rccw9qrr1MX7fpMxcE7r/Hk8gHMGaS8TqXKqN96INaeuo8gj6Z+Aik+knCDnkO8YStXrmx2k5evr29AcOv48ePx7ZtBkS+JybB28aHQqK75x48fF32sgstyIAkTJsTevXtFnyFuT05iQuO/EU//nLQlO2CtjXJW5GTzXXz8bWX4cGsHelfhjiU2ctUfjaMPDQ9lojZSfCThBrMD00wxZMgQpcd8vHz5UlSl5CQSUdVToyLWLj6kWrVq4jvs2bNHnFvSWYb/3aJFC7i6BrHG/3AHq/tXQmr9uLg5amDmqReA602MKUvxGQRbF+Cd7Qo0zsOUOElRttcy3IyYHLsWixQfSbjAm5b1e5hTTWu1aGro4h0vXjz8/fffwktJYh4ig/iw2i2/A1PsnDt3DgkSJBCu+iEuYniOM7MVssXUIcbvNTBlwTIMrpwMicr0xbJl89A4Vzz962ZEo0l78PJ7yR6JghQfSbhw48YNMflnyJABb9++VXrNh+qZ1Ldv3wjJpB1ViQziU69ePfEdWMlUrW7aqVOn0H0fv0+4uKIH/k6gQ8wEqZAhVXzET5UBvyWJA13s7Gg37yQ+SguwJlJ8JOECi7bxpuV5j7l59uyZiMegs0NE7LqiMpFBfBo0aCC+Q6tWrcT/Z8mS5SfLv7vDbm0/5EtEjzClxfsT3Zedxyfp7R8kUnwkvwydC6pWrSpuupUrVyq95oM53PjeFSpU+CFQUGJaVPHhhG2tqLFpyZMnF2eW/fr1Ux75Gdxgu7o3CiWNi2Rp/4fBW24p/ZKgsBjxoank5MmTOHz4cKCmVQmTaS6Mx7HRN98YT09PUVnTeCw9W7Qi4Fl8zHgs24sXL5QR36F5SWusjc2PkVj0xjp9+rTmeMbHGHP//n3Nsew3hs/XGsv30/L64ufTGq81cfN7a401LNL24MEDsfLljTtv3rwfxvLvz9/BGP5exmPZtNKY8DrQGrt//35hs+d7Gwa20navNV7LBZvxHVpjtWKF3N3dNcfyfEBr5U/3Xa3xTMBqDPu0xtL7yhheu1r3C5ubm4H7rwK/i9bYR48eKSO+E9Tf+syZMz94MariwxQ1Bw4cCDReK10N389wjNpotjWGbtBMTms8lilxjFM38Trn38l4LJu9vb0y6jvsUx+nWzO/A1v27Nl/ODPkLsjw9dT2+vVrZYTKe6wY2gaFa/TEqkPHcezo93lHq6ghf0POQ4avycb7RasOVXjcL6x1ZSlYjPgwD1ecOHECLgK17du3TxnxnVGjRv0wjo32WmMYb6I1lk1rsi1fvrzmWK3aNOqK27jx0NsY3iwMvtQaryVWak1548Z+Y/h8rbGJEycWk6Ux/Hxa4w2D6VT4vbXGli1bVhkBzJ07Vzga8MbVGsumFfej2teNG39fYygyWmPZeN3Q2eHWLf/VJidIHhhrjeXEZYwa02HcmjRpooz4DidxrbEMDjSMB1FhOW+t8czAYMzSpUs1xxYqVEgZ8R1O7Fr3C5v6dzCkadOmmmO1VvkUEa2xzJlnfJ6mio9W0wo0Hjx4sOZY5gI0xtbWVnMsm3E2Agq/Gq9j3Ji52pjZs2drjjX+W1MUKaxaY1mx15gFi5ZojuW8YgznH62xbL96v3De1BrLRaKlYFHiwxQXxn8sLRv+iBEjfhjHVqtWLWXEd4ITnx9XLgi0CjJsTDBoDCdrrbGMjDaGK39O0FrjL126pIz6DktQa41lvzF8vtZYOgBoiQ8/n9Z4rZuJ31trbKlSpcTjnOgbNmwo+lg/x3ic2rRuJv5eWmP5+xoT1M2kto4dO4rdJeFn4kSpNU6rzEP//v01x/J7GROU+LBpiU/hwoU1x/Jw25igxCd//vzKiO+wbpLW/cKmZQFo1qyZ5ljWszGGuzitsSyT8TPis2PHDmXUd0aPHq05VqvwH4OWtcay0bXeGC6ItMZOnDhRGfGdtWvXao7lAkqFC8agJnw2rcXa9BkzNMdyXjGG84/WWLZfvV84b2qNZfySpWAx4sOVCy9W7iYMm5ZAMG2/8Ti2CxcuKCO+QxPEpk2bfhi7detWzazLNFUZj2XTMk/wBtAay22zMTQLcCWoNV7LFMRtutZYre07n681lu+n5fnFz6c1Xsu0yO+tNZZ/J8LfIkeOHGIipImJtU+Mx/Lvr2UK4u9lPJaNr2kMrwPjcUz2yPfljnL37t3KSH8oVsbj2QxzdKlwp6A1VmtHShOn1lh+by0zLidyrfFakwvNPVpjtXZrQd0vbFrZvGmS0hqrZe6iyUZrLONggjK7pUyZUhQPNByvZVqk2dhwjNpoJjWGC7bNmzf/MHbLli2aZtyzZ8/+MJZNy1TNz6Y+nidPHvEduAM+dOiQMgJiMcZAUzbulAxfk01LAEO6Xwzh/MN5yHisqe4XNu5qLQXpcCD5JWiWowDwsF/rhjElakYFptPRWkhITE9kcDhgqhl+B8OFHU1iqgm+R48eSq8kPJHiIwkzPBCmrZ436KpVq35YFZsSOntky5ZNOBosW7ZM6ZWYG1V8rNXVmlaDIkWKiO9w/fp1pRdYvHixcN1n3JosSmgapPhIwgzNdzR5/f7775pmSVMyduxYMWEULVpU0zNIYh6sXXzo9abW7FG9xhg3RscD9jFPoMQ0SPGRhAmeJTGHG29QZhVgeh1zwbMp7nr43rT/SyIOaxcfnpcwCzurldLUxt276mTDUgshVi+VhBkpPpIwwZ0Ob1p68Bke0pqDoUOHismhdOnS8qwngrF28aGnKHfu9I6kMwlduDNmzChKcyxcuFAZJTEFUnwkPw1Xh0uW+MczMLOBOWvn0HMpa9as4r0Z+yOJWKxdfOgVSRdymtno5Tds2DDxfehsoBUkKwk/pPhIfhoe9hcsWFAcyFKEzIkaEMpJT571RDzWLj50VuF13KhRI+HuTbdqBmfT3VliWqT4SH4axj9wwqGXkFYsh6k4deoUkiZNKuzzWrEvEvNj7eKjOq706dMHderUEf9mYKk5zzCjKlJ8JD8Fi2v9888/4iadMmWK0mt6aAJRJzpWLNUKnpWYH2sXn+7du4vPz/RDzAiSIkUKsciRmB4pPpKfgpkEeLP+9ddfZvUEUnPM5cuXTzNiXRIxWLP4MOuImvMuUaJE4v+10ldJTIMUH0mooWeZmvuOHmfmgpHnTBQaN25ckdVAYjlYs/gw1ZKa3YCN15hc2JiPSC4+PnB1+QRP/3yTocAbXrLqYJCsXr1aZBSgtxkD8cwBbe9qckfW1I8MTgbfPr/CnSvX8dLlx1xw4cJXb/2Vbx6sWXyY0YBJdrnrYbDyjBkzlEck5iByio/nSxxdOQX/DR2FiVMmY+yIoRgzZyvuOAehQp72OLB4PPr36Yv+ffthzMK9ePJjMugoDd1Q1ahvc571qC7djMWIHGlOnHFiTnvkzpoDtSccglO4nWt/hf2lrZjUryOaN2qIpq07YeisjbjiaNqDc2sWHyZKZVkKnmFSiKSTgXmJfOLjehcr+9bEP1XbY+amgzh78QKO71uOPvVLomSTCTj/MvAN4vvxFuZ1qIBCFVpi+ubd2LtjETpWKooqXefjtqsySIKpU6cKl1TWAtIqHWAKGACYNm1a8b7MYB05+IQTs1sha/I0qDbuMN6Hy3ztiZs7RqNMxnhCCGLHUlPox0fOav2w+6aLMi78sWbx4TXFz961a9eAchwS8xHJxMcbN9Z1Reakf2HInsBmIefT01AkcXxUm3AM79X8l98+4tjo8kiU7G8M3PFK6QScjgzCH0nSodaYw5D645/NQC1Ax7T55oCR5iVKlBDvyUPhyJTJ4KvrOzy99wCvP3khPFKxfr69DR3L5UXlHgtx8tot3Ll9Q7/z/w9lM1CA9AuGVnNx68diueGCtYoPxYa1jPjZ58+fr/RKzEkkE59nWNlZP0kmrID1t4xk4+lhtMuuQ+p6s3FbOTb4fH8dqiTRIVWZ/jhvWB7E6zaGFEmAuJmqYMXtqO3Sy2wGarG1ihUrataKCW84ibVq1Uq85//+9z/NuikSBb8POL12AgaO2gyHQHO/J66t64U/ousF6LdqWHLBNLtVaxUfOhtUq1ZNfPbgatwwoFqrppjk14lc4uP7FCu6FdRfUKnQZN45GB7buF5ZhvKJdSjQewscxQ7bG5dnVEM0XWwU7bQKb8UoFXfs6Z4bumgpUWfSWbMd3loizFzNvFeMgdCqAhrecEU6YcIEMSmwQJlWgUCJAd6vcdvmFGye/mg2+uZwDr3zR4cuTlFMPvBc6Q1frFV8WECQOdzSpEmDK1euKL2BYdJRVkdliXZmv5aEL5Fs56Nf7a3siiwx9Ku9jJUxcc99iNvBzwFrehRHqsx1sNz2jRgJbwfMqcVSy8lQY/RRBHZy+4obs2rqhSk6/mo4HQ9CZQ7+hld3zuPA7p3YtmULdh48j0fvjExFX97jns15nL/yVC99gI/zY5w/vAe79h3BpbuOCDju9HiNa6cOYNfufThhcx8uEeSBx1LNlStXFpMLa/2bw/S1c+dOEehHsaN3nSXg8foOTuzT/65bN2PTll04efURDB3V/L66w8nhCW7YnsdZm5t4a3Bu7fP+Ec4dO4IL995CvYy+urzE1TMnYPvoHbwM7W5+rnhkcwz79u7HgYOHcOLcZdy8cQsv3cNonHO6gfHlY0KXpgZW2Jjm3MdaxYe7HX5uFkHU2tmwCrBabp4lFyhWkvAl8jkcvLuOmc1yIbb+oon2W0kMWboHO+b2QpXyDTD98EMx6ZNvrqfQJVds6KJnQIv515RelW94uroV4utfI3XJnjj6UekOiq9vcHrZCHRs3xn9hw5C384NUTR7BuSv2Q1brrzW75zccf/MNkzsWhO5U6VE/jqjcOTWUUxsVwP5MyUUF3iSP2ti5nF7fLA/h+nd6uB/OdPqxU8vosnyoOOCCzCRyT5IaG5j6WB+NgaUapV9Dm9Y0lk9Wxo0aJAFeB95wf78SnSsUQ7VGndAn9490KRSXvyWrhBaTt6NF4r59r3dZgxtWxk5k0ZD7JQF8d9u/3LkXs9OYHhN/9IPqapOxl2XV7i8ewH6Ni2JjPFioMywg3irKtIXJ5xdMwLtWnXG0BFjMG7cCHT5tywKFqiJBXfC5pLtbX8c7bPpkLbWOFwzkc+BNYoPd9cTJ04Un5u5Ag2dDVgKnY8xxxsfp5v/w4cPlUcl4UnkEx89nvoJfGLTQkiiv3h00RIiY97qmH0p8PT91Wkr6qeOBl3s7Oiy2rgQ2jc839QJKfTPT1iwJbYHG9LijDPzWuHPPypi0gF1a+6OQ6NLiYs3eY0JuObshrvHd2BS83yIqe9Lm68mBuon9kUrNmL/kf2Y37UUEuv7k+Wqib7DBmDYxIXYvP8Qds7vgjxJaLOviY1PzXtj37x5U5glWDKBVUpNDcWtePHi4m/GCY2u3RHN11enMaCEfhJKXgvb1EvE8SjaZNH/JqnKY84F//OvT09ssG/bakzuUVF/zfCAfwlevn2AVQObonb95mjRsC7ajdmOZx8dcWnnLLQpk1F8zwrjTgQ4vzhfXoCqeQtj4M53/h163p1fhMalamDBrbDsOPULqL0DkTNZTvTa+NDfAmACrFF8mIWdFXgZs7Z27Vql1/98p127duL7MH8g61WZM2N7VCNSig95ur0/imZOLiZ7XcLMqN5vKa58v6/h7bgONZLrH4v3B3puMraHU3w6Irn+uQnyNcXWx0q3Bp9urEat9DGQp/s2fJ8uffHGbjWaF8uN4p0W4qayc3I7NxyZddGQunAn7H5p4BDxej2qpYoBXaK8GLjr8XfzG55iYpWMiB4zDXruMZ27rDHM31a7dm1xEzZu3Bhubm7KI6aBxeHKlSsn3o8xF+YKYA2Jb3e2oUlmHWKWGY0b6hzk9RorG6eELlZe/LfFaNHy6Qr6F4iL+Pmro/uwaZgyezMeffLGl88f8NFDPTn0xelZjcTCqMzY48o18w339vRE+pip0HjGaYNdrjuurpuHHU/CsAN0u4dpDfIgf5M5eGTCmDVrFB9mMWBgaebMmXHtmr/Vw87OLuAaZKYDLriYfkdiOiKh+Pjh4Z4JaFi7DebtO4ud01ojexy9yOjioGCbWbiiKMTXd1tQL5V+5xM3J3psNJ7sfPB0dWsk1F+ISQq3w24HpfsHPHF+YQuk1CVE6w3XEGh9+u0LnB2e4ZWzu35q8efduZHIrouBXPWmwXAj7+dxAm0zx0P8zNWxNtC5pjOWN8+F2LGTot36767gpoalg3kT8qD19u3bSq9pYPVI1euInm085LUYvF3w8Mo52D54BY8vX/Bev8PZNKMfKmeJo1+0FNCLj5E5xs8Fx0bpd7yxYiN/i9m44aLlquKO4zOb6K8ZRXzEzscPby8vReUUOkRLmA4V2o/CjssO8KY16JsXPH1+9szHC1eXd0XxUq2x+aGhG2f4Y43io+Yn/Pfff0WC2g0bNoggZvUaPHv2rDJSYkoimfj44aPdStTL8RsqjtgHsVilK+riLvgzHgUoFRrOOI6P+pvaz/0suvwZSz9RZEaHZcYT3lfcnV8P0fUXY/ryA3EuyJXja2wfXg7RdEnRfsNVvRQFD8Unh158ctaaCMMp3df1ONpm1YvP71Ww/IHSKXDCsmZ/6MUnGdqtC1IBwxV6tLGeCSs5GpokTAEdGurXry9u+ty5c4scbpbIpzuHML1/KzRp1x8zFyzG0BppoIuTD0OMxUe/zHh8aBDS62Kh3NDtBjthQ/TiM8NYfPTXo89HnF/cAwVT669J/WMxE2ZE2VajsPdOSAeOP+J0cQlaVq+PKcdehkscUXBYm/hQbOg8EyNGDHHeM2vWLGFi43do2LAhnj83jVeg5Ecil/j42GND7/9BF780ltgZ3vrOODmjBdLF0iFO0T4448Al5TssqJtaCFK9iWeNbtIvOD2CZQNioVCbpQh6z/FGLz4VEUMXDSVGHtK/y494uX6Gm7u/LAUtPseCFJ+lAeJj+ro5r169Ckihw1TzpoQli5s3by7ei7niLNKl2ssFFxZ3R7G/CqPN5N144uqBr+4vsaZlemF20xKfu1t7I0t0HTI3nIprmtZKbfFReXNzH8a3q4QcKfS7K/2YhDmrYdbp1wGeciHh8XAvBjVpiGFbbgY415gSaxMfZuegA02SJEnw559/is9Oz8oRI0aY3LwsCUzkEp935zGyfHzosrXF0cdGdvKPthhbLSl0yWpi8w2et/jh2vzaiK2Lg2LGcT7fPmBl0wzQxUyP1kuCMwN54Nz8tkinv4Bj5+uEQ/bG60xHbFmyBAfs/IXDyYLFx93dHW3atBE3I5MsMgjPVPBgVxWe9OnT4+TJk8ojloQPXhydjKKJdcjRfiWeqTP51zfY0EZ/bQjxCXzm4+lgg6V926BWkcSInr0Ztt3Wmv61xMcbzk5P8eiZmjTVB8/PrUX3CpnEmWWOutMQzLFjAF9enMS4to3Rb/kF/HhC+A1+38JfHKxNfFirh7sefmY2OtWYK2uHJDCRS3zcbmB6/XTQJamFLXeMnZMdsb5bXsTK0hL7FGHyeLod9dPokOyfnjhhmBDB9Sw6/BEPCXM3w94Q5vyPl5ejVqaY+gs5AYp2nI3zTz+IXdTXD49wYGpnNO09E7av/UXp3flR/uJTexIMU2T6uh1Hu2x68WFGhUCL6fdYJs589OJjwjMfuppOnjwZMWPGROrUqU1q8378+DGqV68ubvwsWbLg0KFDyiOWxmccn1Mf8fSfs9CAnd93tU6XMLxMQr345MfIfTTRKAsOP0dsnzkaKw5dxP7RpRAtRm6MFoGd3rhnewPvPNWJ2QMnZjUV4lN27Enldd1x+fAMDBy8K1A6p2/PVqN8kthIU7Qf7IzXNUZ4O9pi/oAuGLnhesAZYwAfb2Pbtv14YB/+K3trEx9WLFWFp1ixYvJ8JwKJZGc+Hri1thsyx0iIGlNPBT6DeXMYXUtkR7kB2/FG9Qzw9cDF2XWRIlEO9Nr0/aT/wdq2yJgkK9osvmbgeRYE397h6NRGSC+SOcZC1qJV0axVK/xbLjcy/lkF047YB7i5Oh8fJHZJmaqORqCQNc8jaJExBmKmK4ulgXY+zljUMDuiRUuMZitNF2G9Y8cOJE+eXNi+ly5dqvSGPzzT4a6KNz6Lwp0+fVp5xBLxxq1N/ZA9ug7RM5RC72krsXr5fIzp3QE1/mYMSCqUqtcGnTt0xsSVO7Bl7jD0nbQXH+CLO1v6IJMuJkoPXY39u1Zi6qL9eOmhXgWeODK5HhLo/waFhx6Fv7O2D+7s6Y8CvxXB4N13Aq45z7uLUPa3dKg28pAyThsvB1tMqp8baTIWQJOe/+G/QQMxYMAA0fr364lW1QqgTKfZuO4c/t5b1iQ+9OJUA0dZMjuo2DVLcPOPCkQy8dHj/gp7xzdE7pyF0XLEIuw9cRqHNy/EwBZ10LDnXNi9DRwz4efxDGv71ED+IjUwbO4qLJ3SG9WKl0KbKXvxKrQerm4vcXheL1TKnUJc2GwZijfB7EMP9Wta4oJr+5ajd+Us4rFoKXKjydCVuPj0JR5eOYDZPSohTTQ+LwmKNhmDrRcf4/nja9g6rR0KpfY3EaQt3BLzd17E63A25Nva2iJDhgziPRjXYKry1IcPH0bOnDnF+7AgnTVEjHs738TiruWQWv+ZdXHSolj9vlix5zh2TWuM1DHjIX2G1IjP3GkJM6FSxxmwcfKf3L/c3Y6Wf0RHtCTZUafPYlx18r/mfFwdcXLlf6iZ3/86iZ2jOobO3Q/7r1/w6PRYFE2SElnzlUKDdt3Qb9AgdG/bGj0mbMRt56B/E+/XVzG9UQ7E4mcMsqVGp5VXTHIGZE3iw2uQGdLpYk0vSy3mzp0rdkQrVqxQeiSmIvKJD/nqggdndmDxnBmYMWM25i9Zhe1HbPHicxDHtp5vcWn/GsyaPBnTZy/BnosPwpDSxgtvn93D9ct2uHz9Np6/Myx65o33Lx7gyqULsLGzg82lS7C98gBvXd3w6f1L3La7iIs2drCzuYSLl67i6dtPcP38Hk9v2uCCfqydnS0uXbDBnedv4RHak+dQwJVfkSJFxOTBzNE89zEFrD5Kcx7fhxHjjOuxFnxc3+Dedf1vZnsFDxwUU677G9y9fgP3Hl7B7pXTMH7mWtg5GOyzv7nixoFlmDFnNS45fL8OfL+649WD67C9dBG2+uvg0kUbXL/7Am6+3+Dl/g5P797DrauXcPbseVyyscHlW0+h6a1twDeP97hvdxYXeP3oX5OLiUBN32d39QHeuZlGGKxJfDp27Cg+K0soGMNdUc+ePYWXJ8dwISYxLZFTfFR8veH2+TPcv4RuNe/zxQNfLPv+CTeYz0o9e+FOxBSBnfRooxcRz5L4Pu3btxfu1ZELPyNPyaiFtYiPo6Oj8Kqks8GxY8eUXn+4CKtatar4Hgw+Ze0qXrsS0xJpxee9szN8ZISyJhSABg0aiJuN8TUs2qbCm45CxJXgr8DIcXViYp6s4cOH/3JiUpbQdnExX6YHyY/QLMsSF6rZSi1xTvExlck2PGDhOJrcChcuHChnILO28x7gd6BZmNVNJeYh0ogPJ0uWWT548KAo88zElHTplQSGfyfuQHizMar7xIkTyiP+MPUI6/a0bt1alLA+c+bMT5nJuPplNmra1fkePODdunWr8ujPw9gjiuP69evRrVu3X3otya/DBQBLXpQsWRLTp09H/vz5xe/M39tS4WfmNc3PuXjxYtFHAWKAadKkSUU/H2diW4n5sFrxoXswU7Ew9TndhBk3wuAxXkhsw4YNExlqJd/hTcjobv59eAazf/9+5ZHAqIXc2LhroVmOz+Mh7Pnz54PcfXBF3KtXr4DnNmrU6KfT8zAIkO/B3FqMQGdJB/W8iDFBcoKIeBiXpWZ9VhuDNilKTF3DyreWBK/zZMmSieuIiULZeO7Dz83dEP8tF6rmx6rEh6kvKDZjxowRB+QFChQQWZcNbwI2xo9wFyT5DqO3uRukzZtu1Vu2bFEe+REW16Lt2/jvysYVLjMCU4zoSMAFgKenpzBXlC5dWoxh8blp06aFynRHUxwPyunizbLGtL2ruybDxnOjUaNGKc+SRCT8vdXsz8aNokQnFu6ceXbC8xUuKCIKlgbhjpmfjeePXLyo5mAWK6Q5LuJLd0RNLFp86G/Pok+cdOrVq4eCBQuKQmOGF7tWGz16tPIKEsLS1/Tk4QTOG46JFEOiRYsWmn9bw0bhZ/0dZgOm4LCPcTzBxe9wMuDCYOXKlWLFWb58eeTIkSPAyyioRvOOXJ1aDjRvq795cI27VWYqpxgtWLBAxHqZ82yIYpMtWzYkSJBALJg4h/Bz5cmTR3wHScRhMeLD9OUUG0a8U2yY6Zi5lzhZGl/QITV6tXD1xQy1sv1PHKjSvMC/DfNYsS+kvw/Tjhj/XUPT+HvxEHrcuHHCPEMTx4MHD4TYdOrUSYgTdzacDLSeH1SjbZ7xF1qfVTbzN15TcePG1fytgmocz+uK+QN57kjTKjNemNI8PnLkSPHe3O2r1xx37vfu3VNGSCIKixEfVgvs27evuKhpnzW8aGWzvkb7eokSJUS+OJrS6A0V0u5GtqjTuGvmjqRJkyY/uD6HFzQJq8lD2bjzZ3odWSDOMrConQ+DHOmPz0NLHjbzoJsXqPHhZkiNZz5cJdOtMqo17mh49pImTZqAvweFQGtsUI2voR7yh6ZxV5U2bVphgqMLN72g6DTAm5xnTTz7uX79OhYuXCgcQ5hahwW7DBM8htRY5oG7Jq3PK5t5G68PejGqu+nQNP5+vJd5bVIANm/ejKdPn4rrwxTxQWq+Qr43TbZ8X57vyAJxloPFOxzQZMPtOc8HypYtK4TF+MI2bsxpFZW5fPlyQElqCgLTivwMPFAuVcq/DHhQjfZ+TkL0aKOXE122ebYUGrjIYHZh1spnPR+aYWgW0XoftXGyCyoXl8T8LF++PNidLE1sLEZIF2aeN7I2FK0b5oKxanx/mpnpXEPR4XmjxHKwePExhK7CXFFzBcNUGVzNaJ0JMVeZWh43qrF9+3Zx5sW/Q4UKFcL0d9i2bZvmqpbnLiy4xTO5vXv3il1qeGBvby+Sm/J1+fo0vbK+vuF7878HDx6sPEMSkTg5OQWUnFYbrxfubOhJprrlm9u5QIUiM2PGDPG5aPKVZjbLxKrExxjGlXBVz2Axun7SnKPeDMzNFJVcKOmyTDODGjTHWB0Hh5+vfsoU8/QEUv+ObNw90YOQnoem/pvy9Wmi27hxo8iKUKtWLWGi4+fg/9MNXBKx0HzK34PneOr1RjMtF4ah3f2aEu6QuQDluRIDniWWiVWLjyGcfBmdTzFifAFNb0Flro1sMKiPcU+qWFB4fyY3FUV83rx5qF27tnCNVV+HXk3M8suD24iCq2wmyGSGgy5dumDTpk3KI5KIgPcZd72c1LmzUXdANIdbCmqgMz1mfzVNlMR0RBrxMYZu21Ehw8G+ffuEmYo3G4WD5o6QDnBpCmF+N5roGjduLNLsqGY22upp+uIkH5adkymRud0iHp6dGJrSWBeH142lJBZlOXa6VHNHFtqzTnkWFDFEWvGJ7HBnM3bs2IAMDzzYDep8h5M2AzRtbGyELZymLENvNh7K0juQ5kvuokxVWsFcfHN3wuMbNjh56ACOnL6Mp+8Ny1sY8eUjnt26iCP79uDo+Rt48d7957NUf/PAuyfXcfLgXhw8cQn3HT4GFBDU4puHMx5ePYeDe/fhpM1dvP74awlXIxJLympNYeTunZ+HLv5BiQr7mXWB9wvPGRniIQOYzY8UHyuEIqLe9BQRBnSqq1EKDcsl0EuQ45gclNkKjING6ajBMzKaJ2nWsoRVa3jg/uI0pnZtiNoN2qFP765oXKEQ8vzTFLOOPv2hKu2XNzaY1ak8sqZOgkRx/R0cMhRrhkVnHBHqY3J3e+yc0AqFMqVAogT+3l/xspTH4A12cNX4k7o+PY4xzYohQ/IkSBCbv0Vs/FGpGzZf8y+/bm1Ykvhwt86FFO8JrSBSOshwZzRp0iThMq7eC2w0IUrMixQfK4ICwxxohgfwtG8fPXpUpMxhzjumMWE6E8M4HzbVNZpnQ8y7xsPhXy1xYGn4vLfF6Bp/4u+6Y2Dr5F9175teYEZVz4hY6Spg1rk3AaLi9fkhVvf/FxXqtMfImQsxb/IQ1P9fWkTT/62SFmiPA46hiAf59g4n5vZAtSr/os/oGZg3azw618iHJPybp6uI2adeBRIxd6fLmNOlOio16IZxsxdh1rg+qPqXf0B1hopDcNEKLYqWIj7cufCMkp+FcWYq9KRk1hQu0HhfqPcDG+8fpndiTKGlmZijAlJ8rAS6i/ImURN+0vU4e/bs4qY3vKHYGH/BA2CmvacYscQE65a8e/dOebXIyGecmVYfKWLmwLCjgUtAvDs1E8UT6JCm2gRc/0RR8cWryxsxftImPDbQ3y8P1qFelrjQxUyHjutfKr1B4/HoEGZPm49jzwxe5OMljKnBsuSxUHXcPjgp3fD1wIOTKzBh5h44GGxxnC/NQunk+l1X0vwYcdD6Cu1ZgvjQ3MakufwcDExnnBtd9//7778f4tXSpUsn0j/RZM30TzKpaMQhxcdKYA4sw6SqNC8wMJOBdFWqVEHnzp3F6o7Bf3RCYKZoerFFGT6cxX8VEkOXvB523DXaQjidx7DKyaGL8TfGH7fX70Z84fH+BV794AjljtVNMyNG3LTouCHkv53n29d46+JmZC7zwMWlTRFXFw2Vxx/Ae6UXvp749O4l3hofp/m+wrQKCaBLlhcjD0W8m/LPYgniw4UVzchMn8OUTlx0xYoVK+Be4a6/WbNmmD17tgglsPYzzciCFB8rgSs03jg7d+4UXjzMHM2zGtq2aXKI6rWLPK6uR6PM+skmfVPsuWs0ifs9xYruRRFNFx2VppyBS5CHK5+xpFF2pM7TBHscwpqGxR2nZ9dB0sTFMOXka4T4Kt72GFsuJdKX6Y1z1qc9ES4+LDZoHPDKRm83nnXS+5P3iSyLbXlI8ZFECj5dWonaGfQTT/xKWHrZ2HPpNTYProjY+knprx7b8DoIS4vP861oW6Eahm69F3qHA2Pe22FSy4poMPoAnEMxF3+6thgNytTF9BOO+v1Y6HG5fwzzRvZCu1bNUL9GZVSp2wGzdl/DJ+VFvn5xwVPbXZjYtQ4a9Z0Hu3deeH58EXrUL4P8eQujZtfJOP6EfwgfvLi4GcPb1kCRfHnxT70eWHXeIdTODxEtPtzt8/15nkmTG880mTeOMX9ScCwbKT6SSIHvw11oV4CJStOi/dqbRuLxChv6lkJ0/ST1R6eNeO2pdBPfb/ji6oxX945iTKMiKNZsOq59+BkZIL7w9viEdy+vYkW/WihSpi02PwzGtOP7FR6f3uPF1R3oU70AynVbhaeGnylYfPD86HT8W7ICei44jEf2z/HMdgM6FE0CXZws6LjCFm7ffHFr51R0qJEH8bkL+Kc1xk2bg/4dmqFV62Yo80di/d8pFgq1GIsN2xahe/3qqNu4OeqWzolY+vGpi7TH7heh2/lFpPjQ0YYxPTS3sbw6xYZ5CSXWgRQfSeTg6xOs7FZECEyK8kNx1vG7gHg4HMGQmv757ooNOQgnA2X65mKPY8uHoGYBfw9CnS4J/tdkAs6/+Rkz5kdc2TkPXar+iTjiNXT4vUw7bLj+QXMH5f3uPnbP6Ylyf/inptHF/A3luizCLZeQJ3zvZ9vRumAa5Gm9Go4BH/ETDk/6F0mj6ZCxxVI8ddV/r69f8PjUVBSJoUP09CXQd8UFOLh6w8fXDx9vr0XNtPr3jZUWlXsuxtnHH+GtFyxf9/uYVCm5vj8zOq0KXRLQiBIfJg5ltmq+NyvgMou1xLqQ4iOJNDhf3Yz2Rfyra+ao3hPzVq/G6pVLMKFnI+RNRVFIiTarrsIw5NTHzQn3Lh3G5qVT0KtBSaSLy3EJUbrPNjiH1vbk54Zn1y9g34YFGNGlNnKl9o/3+b3OJFzRsL15uzji5rn9WDd/nH53UhApouvfM0Zq/DvhOII3FHnh3LQGSKsf22OffSDTmNvzS1g3axrWn3kKT+WBj7c3oHpCHRKUHoBThpmmPj/GuFLRoUteApOPGibd9MaJIYWhi54adSedVfqCJyLEh+efdCDg+zLTfXgluJWYFyk+kkjFuxv7MLlHY1QsUQhFStdE+yGTMG1UVxRJpp/gk1XHyqsB/mc/4uOIXSMqI6l+UkvwZ0NsDpOzoAeureiFvCn07xe3GGaceRH8WY7bAyzX79ji6t8zdemeOB6st/VTzG+dHzF0f2HC5ddKX9A439yAGol1SFhmIE4ZDnd5gskV40CX4h+9+Bj+PTxxZiRjYVKh1rgTSl/wRIT4MI6H78lYtosXLyq9QUNPUSYblbsjy0KKjyQS8hUfXjvA0YnnLl44O6MWEuknqxztl+JJSF6270+ibbYY0KX7BzNCnte08b6P2S2y6yfI39Bj9239fiJ4vB5vQw39ziyGXvDWB5vD9RamNMylf9006HPAPkRPuu/iMwAnXymdxOUxJiniM+lIQCSSHk+cHlHCosWHbtX0ZGMhQnqyBcWLFy8CSrczm0GlSpWiVuiBFSDFRxKpcX+wBU1/14tJ+oqYf94pZNfnb85Y0TAt4matjCW3lL6fxgPHp/2LxLpMGHT4UchebK6PMbFMfMQv0Bq77JU+TZ5jUbvCiK6LhkL99+HHhAjusDt2Co/e+hvvPtyKXOLDUhss78H3Y4E6Yyg4zADCxLh58+YVjggcy8bS/Ldv31ZGSiwBKT6SyIvnUyxv/ydi6n5Hi1ln4BYaq4vPG8yunRlZKg3DlUBbFl989fLC11A5gbnh4OjKSP37v9h6303pC4ZPt/HfP6mRu9lcPA7Wx9sHF2Y1w2/6yTRamoqYe+GNwbmPL5zOz0ePIQtx1dFfBD7c2oiaQYjP5Era4nMmQHxOKn3BYy7x4a6FheH4XkyMy8SgTDfFUtyLFi1CjRo1AmVnZ2MQdpMmTbBu3TrcuXMn0qWTsnak+EgiJ96vsX98baRNmAF1R2zHq0Ci4Ysvn53g6PgGLurpvMKbi3NQNX8x9NnwwGDH4otnB6eiQfnSaDJsG9T4068eLnjr6Ih3nwIHDnk/3YOu5fKh5sh9eKu+iN83eLi8hYPjW3wOJGrf8HDvcJTMWx7jDr0OMb7m25Od6FDYP9NFgpxVMXTxTpw5fwqbZ/ZExf+VwYCNV+GuvKfr/c2onkCH+GUG4pzh0c4XB0yrFEsvPiUx9URgF4eLo3nmkxK1J1iOw4Gbm5vIUs33yZkzp3CrZj2hypUrI2HChKKfjaY4FpFjcClLZzNfm3S9tlyk+EgiDb4+XnB1dsS9KyewaEgTFC5QGt3nHf+e4kbFzxUnJlRHysTpUKrFMKw7dB42NhdwatcS9GpYHW0n6UUjkAp4Yu8A7gj0E9wfHXFMSctzf8sQFEmdEDnKt8OsLcdw8dIlnDu+GaM71kPdbnNw2dl/nMDrFbb1K4FESbOgSudJ2Hb8AmwunceRjTPQoU5N9Fx0DqEte/b8yAzUy59GxOSoE2+C1NnRYMwO2Iu51hefHe9j//y2YpekS1EGYzddxfP3HnB7/xI3ji1Dbbpa63c49UdswS17Z70Yv8fTWycxqrJ/otMsNYbh5H0HuHoFL4emFh/mbWNxRPV75sqVK5Dg8N80xVGcmM+NORBlfR7rQIqPJHLg44IHF/dh+ZyJGNi1Ndr2mYRdV4NIpOrnidvbRqJGsXzIkSUTcuYtjur1m6Blh76Ys+MatAxlTnYb8V/Xjhix/CxU52THC2vQrWpR/JU9MzL/UQDla9RHs1adMGLxYbwwXnB//YCLK/qgXOG/kS1zZvxZsBRqNWqG1l2GYPnRhyE6JRjz8d5RLBjZAy0bN0LzjgOwYO91fAqYc33w7Mx6jO/fDg0bN0bjhq3Qe9g0HLj5Bo43j2PJxN5o0Ujfr3+sbffBWHzoNpyf3cKe5WPRsbl/f5PWXTBu3UnYf39RTUwtPjNnzhSvT8825jDk7iZx4sQiYWi3bt2wa9cuiyjdLfl5pPhIIgdfP+HpzQs4cdYOT96FztTy5f0z3LxiCxu7q7j77F2wBeCCwtftHR7cuAxbGzvcvP8Cn0M4E3J78wjXL9vC9vI1PHhhnTV8DDGl+PAshwl0maWddal4vsPkoNzhyIq21o8UH4lEEmZMJT7Mzk6TGkuHsE6VLH0Q+ZDiI5FIwowpxIfOBGrdqmHDhkkvtUiKFB+JRBJmwlt81q5dGyA8gwcPljueSIwUH4lEEmbCS3yY+mbZsmUBwtO/f3+544nkSPGRSCRhJjzEh89jvjZWH2WQaL9+/URsjyRyI8VHIpGEmV8VHwaBjhgxQrxG3LhxMXr06CADQ5nV4O7du3JHFEmQ4iORSMLMr4gP43N69eolns/Ynblz5/6QeZpCdODAAUyePBl16tQRNXwePHigPCqxZqT4SCSSMBNW8WGZAwaz8rmpU6fG+vXrlUcgcrYdOnQIAwcOFK/PpKAcp7YzZ84oIyXWjBQfiUQSZsIiPidPnkSRIkXE83LkyIHDhw+L/lOnTomsBf/88w9SpPDPX6e2okWLingfls6m+U1i/UjxkUgkYeZnxIcmNQaPpk2bVjynUKFCmDFjhvBsy5cvnzC9qWLDNDrFihXDhAkTRMG4169fy5xtkQwpPhKJJMyEVnyY8PO///4LEBfmakuVKpVIn6P2sUgcdz0TJ04UtXtcXV2l4ERipPhIJJIwExrxsbOzCxiXJEkStG/fXtTe4X/z/ytUqIBJkybh5s2bIou1JGogxUcikYSZ4MSHO5f58+cjXbp0Ykzu3LlFUlDCRKHjxo0TOxxJ1ESKj0QiCTNBic+NGzfQvHlz8Rhbq1atRDVRiURFio9EIgkzqvhkzpxZ/DfPaOhU8NdffwWI0uLFi2VFUckPSPGRSCRhRhWfrFmzCq+0Jk2aiDQ57KtXrx4uX76sjJRIAiPFRyKRhBlVfOLEiYPffvtN/DtLlixit+Pu7q6Mkkh+RIqPRCIJM6r4qK1s2bI4ceKEcK1mOQQ245Q5EgmR4iORSMKMofgwZidDhgwoUKAAypcvj0aNGqFnz54YNWoUZs6cKUombNmyRaTOYYqcCxcuwMbGBvfv34e3t7fyipKoghQfiUQSZkqVKhUgPozZMQ4cDU2jWD19+lR5RUlUQYqPRCIJM+vWrcPw4cNFVoLTp0+LXc3WrVuxatUqzJs3TwSPsmTCgAED0LVrV7Ru3RoNGjRAtWrVULp0aeTNmxc1atTA+/fvlVeURBWk+EgkErPBDAYsFOfk5ISXL1+K+jzMcC2JekjxkUgkEonZkeIjkUgkErMjxUcikUgkZkeKj0QikUjMjhQfiUQikZgdKT4SiUQiMTtSfCQSiURidqT4SCQSicTsSPGRSCQSiZkB/g+VSGPXja9bSQAAAABJRU5ErkJggg==)
An equiconvex lens
of focal length 20 cm is cut into two equal parts and one part
is silvered. Another concavo-convex lens
(radii 10 cm and 20 cm, μ=1.5 ) is placed with its principle axis 2 mm above the principle axis of
A point object ' O ' is placed at a distance of 80 cm from the lens on its principal axis as shown in figure. Find the position of final image.
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)
physics-General
physics-
A point object 'O' is placed at a distance of 30 cm from a convex lens ( f=20 cm ) cut into two equal haves each of which is displaced by 0.05 cm as shown in figure. Find the position of image? If more than one image is formed, find their number and distance between them.
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)
A point object 'O' is placed at a distance of 30 cm from a convex lens ( f=20 cm ) cut into two equal haves each of which is displaced by 0.05 cm as shown in figure. Find the position of image? If more than one image is formed, find their number and distance between them.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcUAAADeCAYAAABMpxtoAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAEiGSURBVHhe7d0FWFRLGwfwFUVEBRFFRey8dovX1isqKCp2d3dgJ4rYid3dYgcqtiIKBogKKI20dMf/O3M4uwISu7CA8L2/55nnXudsHFD2z5wz844IhBBCCOFRKBJCCCECCkVCCCFEQKFICCGECCgUCSGEEAGFIiGEECKgUCSEEEIEFIqE5LS4MAT+ChP+QAj5m1EoEpJjQvHpwSlsMV6NZYuXYNNxC7iHxwvHckmsP2xf3MfVSxdw8epNPLF24s4qE3F+sDG/hCMHDuLU9edwoTwn/0coFAnJCbE/cXfTRHTXGYQ1B85gx7jmUFKqgsX3A4QH5LxIzzfYPrEbqhYXQSRKaqVqtMbwFSfwyT9BeFRK0V6W2DatP/QMxmDhsuWYOUIf+uON8eh7pPAIQgo2CkVC5C4SVntGoHa1Flh624vv8by+Gv31h+OIdQj/55yWEOyIPaMao0yFxhg6eyU2mKzEJP0mKM6HY0l0mX8S36OFBwsSQuyxo38dlKndCwc+BCV1ephjYhMN1O67Gpa+SV2EFGQUioTIWdjno/hPSx0tJp/GL6EvLjwQ3j5BiBH+nLOi4XR3PQx6T8OFj+4IFwaFkf4OOL9EB2osGNXbYtOjpMBOEg3boyOgKlKB3toHSH6R98uRwVAWlUFfEwvQlVRS0FEoEiJXATgzsQEUSzeB0eNM797ljKhAvDlujF3PAoWO3xK9n2BqIwVutKiJUTueI07ojw95jyUti0Kk1grG5imfF+p0El2URSjRbBxuuSYKvYQUTBSKhMhNLDwerkNzlSKo2GU57ITe3JYYF4cQb2+keaE2+idOjq7EhaIWxu5+KRkR/rLciEYKIijVNcCZb0KnINbvHeY15UaXyo2x9LKT0JuWaAT6eMLTOwBRQk9KCYgOD0e05HZmPMJCwrneVBKjEBqRO2NqQlKjUCQk28Lx3eouDpssRO9GpfkJLZU7TsbRm0/g9OdgLW9F/sSxoeUhKqUN4/s+QmcivuwbBGXuvMtqT8ED8TVfsRBnbO2tyn1d6hhgci+NS6hh+PLkArYbLYWh4UIsXLIcJvuu4ksAF7nRIXCxfYY7l09ih/EyLDQ+Dw/uGfH+djizfjaGDx6HtRfeIlgYsvrb3sHm+RMwYuJymH3wkYxkCcktFIqEZFswPtw9jvUrJqNjNVUUUdREjynLsH7vebz3Fh6SibioX/BwcYazs3TNxc0HYXFpzyDNSHzAa0yppwyt7sthI8ylAWJwb5E2CrEw77oUVqlXjYS74eBwNrosjA5zTsJd6OYFf8XpVaPQXrszRi3cjLN3nuLp5fXoUL0y+mx6idhwX7x/cBJzdWvzvyxUHX0W3l7vsX/eUHRqXAOludGpqMEMWPrGIeDzBcwb3BUNq5XhH9tl9U340tVakssoFAmRl9jHGNdYHcW0BuNehNAnJX9LUxhoN0Wjxk3QrFmzDFuTRo3QsvNM3PIMF54tPWezWahZrjEWXHHhxodiUTg3uR4fRLV7GcNW6JXgQvHIqKr88RaT9sNR6EbIZ+wcpY2K1TvC2NxJchn08+Ex0FQuhvaLzSUjvddbBqJiEVUM23sbx40MsfKYBT4/OoL+NblQbDQHFs+vY/PCxTj86BXuHBgPDe692i67Bi8KRZLLKBQJkZPAu8vRsHQhaOjugKeMa/SjfD/jwfWruHLlKszMzDJoV3H1yhVcu/UKbuEyXlwMscaK7vXRbupxeMQKfbwonJlQlw+9uvomsBd6JcLccGB4Zf54y8kH8J3vDMLt5d2gplwJE09+S3Ff0On+Pqwy3oNnrsJvBglfsWVIAygXb4O5qwyx6uhTflZuyIudaK8qQrXhRti00hhHLdy43mg82dQTRUVlMeH4m3TuTRKScygUCZGLBDxe1wdlC4nQeZ0lUmTOXyEMD0wGo43eAlh4pQ7TGFyb24wPvZq6Rvgk9EqEuGCngQZ3vAg6zjsFdkU42mo7Wpcpgoo9jOGYxi8AyQd4id/OY3B9JYiqtMfUVefwg8/KUDzcOgBqotLoNHAM1l6xTpoYFPgJJjoqEKn3wNE3uVfogBAxCkVC5CHBAVsG1UNhURUseSTljcRcEwtHs9Xoozsep6zTmvkTD5uteijChaJWJ0O8SrWoP/HXN6ztyoWaqAwGbnzIRWgsrs9ojWKFS2Hk0YxmozKJcLi0BA2URVCsPxrn7YU5saF22DGEXZJVRbvxu/ElMClZAz+eQc9SIpTutgKv/fkuQnIVhSIhcpDochUjm5SASGMgbnnKXhIt7Mdj7F2/FkZGa7F2bcbNyMgI67acxaegVOmVpkT8fL4Ho/uNgqmFc4oRXHIBFstQnQtFlSYjcM1T6BRE+7zEtLoiiIo1xnKzn0DcG8xopQEFZW2Yfs7kAmeiDy4u7YpiIiV0WWuOIOE6a9jnqxhejb1mE6y8+V249xiNT2fHo7RIEd2WXQZlIskLFIqEyIHXrbVopSKCmr4pXGWf/4JAm+OYpN8TPXtK13oNXolHPpnP5vG1OY0pA4bC5Lr9n5d0Y6MQGhbG3w+MC3iGqbUUICrfHtuepwz1YIej6FRMhOLNRuMml4nwPIc+tZQhUumBsz/TuK8Z7w9n919JAez7Aku7luIeq4PjH8Sj1DjYmxmiKhfCZXuvw3vxLNhob5ybWB0ipYZYesVV6CQkd1EoEpJtETDfMADq3Ain9643CM/SjMlEJCYkIEHKlpiY+Zv4f7qM+aNGYZ3ZV6Hntwh3KxzeaYprlm5JC/gTovBiqy6UReUwbPvLFAHqeGoEShRSRc9V9xHMOn5exuC6xSEqUhOLJGsdBaEOMNu/DWdeePCh6P9yP7pyvyyU7bsd4iuniPXGtYUtIOLea8KB15LJNDE/n2NKLRGUm03C7c+esLF6D7cAGScTEZJNFIqEZFe0PbYPr8WNcLSx961Pupcoc5Pv+3MY06wMlFQqoa1efxj01pWMMnV76KB906qo1X0O7jr/vvwZ5/cahu3Lo2ybmXjEVthzEvxeYn7bitDsMAcW4lFhnAtMhzZAYW6kV7rRAGw4eQvPXz7DjeObMHfyNKw59Ag/+YKroXi6eyCURCUxaM8LyaL/WC9LzGssgqhyf5z++Pv9fd9tQRPuNat0HIHVu0yx9+xT+ITKOI2XkGyiUCQkm+Icr2NUXRFUuq7Dp8DkixPyRozPUyz6ryZKFFGAoiKrc8oF0B9NHX3X3kwa+SUTan8Z03u2Qrt+s7B+y3pM7duO+/8FuGGf8pHBH89ibBu2oF8ERVUNVK5aDQ3aDcS685YIEFdoC3fE4bG1oFRRF0fe/L5D6GuzDx1UiqHRqB2wTzYQ9HqxDo2LFEHJck0xacddeIb+fXN4ScFHoUhINjnfWol6iqoYcsAKMq7ZzxGJsaHwdnOFu6cXvLzSa74IiUz70mS0vwOeXDsO0937cOrmK7gHp1WHNBHhPl/w8PwBbDJej12nbsHGJShlWbaEWIT6c+/lE4ToZAO+uOhgeHt4ISAkMsX6xrgQZ5ifOYwzt63hH5X3v1yQ/08UioRkR2IAri3thAoNx+OuS8Ea2Uhz35KQgoZCkRBZxPji/ZM7ePQ+ad1CvPN1jGvTBKP3v/0rRomEkOyhUCREBtFv96CzVgl0WPsK0YFfsX9OX/Sevg8OubOhPiEkh1EoEiKDmB83Ma1jDdRq2x8Tp8zEQpMTsPGmZQOEFBQUioTIJA4BznZ4afEQjy3t4CfnvXBjYmLw48cPBAennhdKCMkNFIqE/CU8PT0xZswYVKxYEZMnT8anT5/g6OiI6GhpyrkRQuSBQpGQv4CdnR10dHQk6wjr1q2L2rVro3jx4pgxYwZCQ0OFRxJCchKFIiF57PXr12jatKkkEDU0NLBmzRrUqFFD0sdGjoGBae1wQQiRJwpFQvKQpaUl6tSpIwm/atWq4fr16/yxbdu2QUmJbdmUdGzKlCl0r5GQHEahSEgesbKyQr169SSh16hRIzx//lw4Cr7w96ZNm1C0aFH+eJEiRfgRZGwslT8jJKdQKBKSB6ytrdGkSRNJIDZo0ADv3r0Tjv4mDsZChQrxjytZsiQOHz4sHCWEyBuFIiG5zNbWFq1bt5YEIrt8+urVK+Hon+Li4rBgwQLJ49XU1HDz5k3hKCFEnigUCclF3759Q7t27SQBxybTPHv2TDiaPjbJZsSIEZLnsXuP7H4kIUS+KBQJySV+fn7o3r27JNgqV64MCwsL4Wjm2KL+Tp06SZ7fsmVLuLm5CUcJIfJAoUhILoiPj8esWbMkgaalpYUHDx4IR6XH7kX+888/ktdhi/1ZFRxCiHxQKBKSCw4cOCBZXlGqVCmcO3dOOCK7e/fuQV1dnX+tYsWK4ciRI8IRQkh2USgSksPYJdLy5cvzIVa4cGEsX74823sVGhkZQUEhaVf9mjVrwsbGRjhCCMkOCkVCcpCTkxP+/fdfPrxYMzAwQFhYmHA061jZtx49ekhed/DgwbSwnxA5oFAkJIdERERg7NixkuBii/O/f/8uHM0+NjrU1NTkX5uNGnfs2EG75ROSTRSKhOSQffv2SQKxdOnSWZpYk5n9+/fzlW7Ye1SpUgUfPnwQjhBCsoJCkZAcYG9vj1q1avFhxUKLjeJyQkhICIYOHSoJ3+nTp/OL/QkhWUOhSIicsVCaNGmSJKj69euXo/f7WDWcChUq8O/FysAlr59KCJENhSIhcnbr1i3J8gu2HlGaijXZwdYpGhoaSkJYX1+fioYTkkUUioTIESvHpq2tLQmopUuX8gv3cxqrp8o2JmbvyXbVuHz5snCEECILCkVC5Gjt2rWSQGRl2Dw8PIQjOS/5e7NlILRbPyGyo1AkRE7ev3/PzwBloaSsrIzTp08LR3KHp6cnWrRoIXn/Y8eOCUcIIdKiUCRETmbMmCEZqQ0YMCBXLpumxma5ipdo6OrqIioqSjhCCJEGhSIhcvDx40d+GygWRmy/wzdv3ghHcpe3tzdq167Nn0eZMmX4OqmEEOlRKBIiB2xCjXiUOGTIEKE3bySfiTp58mShlxAiDQpFQrKJbRxcv359PoTYzM+cXoKRGTs7O34nDnY+rIAAG8USQqRDoUhINm3evFkyMuvfvz9f8zQvsTWKw4cP58+nUKFCMDExEY4QQjJDoUhINjg7O6N58+Z8ALEJLnfu3BGOSCch4hc8XH7gh6sHfPwDEBAgbn7w9nSD8/cfcPUMQLTweGmZm5vz21Sx8+ratSu8vLyEI4SQjFAoEpJFbEeK48ePS0aJvXr14hfvyyLa+SVO7F6HBdNHo4/Of/jvv6TWqUMX9Bk+GYYr1mPvmafwlnHzCz8/P0kRAVVVVTx58kQ4QgjJCIUiIVnEFsezuqbiUeKpU6eEI7KKg7fNRQz/R1ESsMWqd8fay2/gHSk8REas/uqqVaskr7d161baVooQKVAoEpJFnz9/5kdhLHTYXokODg7CkSyI8sL23mWEECuPkXteIEY4lFX379/nJ/6w12RrFtllWUJIxigUCckiU1NTIcREmDVrVraKcEf5PMSEuklFxAtV64dT1tkv0ebi4sKXmmOvWaJECb7iDiEkYxSKhGRBdHQ0unTpwgcOK6l2/vx54UjW+Dxdg4bKSQFbrZ8R3oUIB7KBVdRZsGAB/5qssU2PCSEZo1AkJAs+ffokWQvI6o2yWahZF4vna/9DMT681KG/+gaChCPZdeHCBcksVFZ6Lq+XixDyt6NQJCQL1q1bBwUFBT5spk6dKvRmUcw3rNPR5F9LpN4aq294Cgeyjy3c/+eff/jXrl69Ovz9/YUjhJC0UCgSIiN2WbJ9+/Z80LDR4sWLF4UjWRPrcBg6FZMmxJRuPR43fgoH5IDt+K+np8e/Npt0Q9VtCMkYhSIhMmKzTCtVqsQHTZMmTbI9+nI8MgZaRdml02LQHn8QcsxEnnj3DjayPXHihNBLCEkLhSIhMmKTalRUVPigMTAwEHqzKgBHxzZDUe61RMo1MfGwvdAvP9u3b+fLvbHznTt3rtBLCEkLhSIhMlq8eDEfMqytXr1a6M0i/zsY1zxpfaJyTT0c+SL/PRhZ6Tm2jRR7j86dO+fJPo+E5BcUioTISHyPji3cv3HjhtCbNYF3V6JZ2aRRXE3ddfiaIByQIycnJzRu3Jh/j8qVK9NkG0IyQKFIiAw8PDz4+4gsYKpUqQJ3d3fhSFbE4v6q3ijDvZaokBr01r0Q+uWLlXzT0dHhz7ls2bKwtrYWjhBCUqNQJEQGbCf7cuXK8QHTtm1boTeLom2wWr8W/1oKpZvB+GX2q9ikh61RZO/DRre3b98WegkhqVEoEiKDLVu2SNYnzp49W+jNmiibw9CvLSzFaDETr8JyrmA3W0vJ3kdJSQnHjh0TegkhqVEoEiKD6dOn8+HCdsXIXrgk4P3h6ajDL8VQQItZZggTjmQoLg6xXJM1PleuXMmfN5sctGHDBqGXEJIahSIhMhDvaF+8eHFYWFgIvVnhhqMz2kKRey1RkaqYc81N6M9A/A9cPHwYN9/IXvFm9+7dUFRM2pqKlmUQkj4KRUKkxPZPFM88LVmyJOzts7Gm0MMcM9sl1U4tUnUIbrhlXpPU/f56DB6xALe/Jy2piI0Iga9PgFRbTLEaqOJtroYNGyb0EkJSo1AkREqurq785BoWLGzdH9vdPqvczDfjXzV26VSEyoP2wD2zTPz1Gst0W0F/2QW4B/vhy529GN+rLbpNOgQv4SEZYaPa8uXL8+/XrVs3oZcQkhqFIiFS+vDhA+rVq8cHS/369fm6olnzC7fW9kBJ7nVEoiLQ22qFaOFIWhKDHXByXleolmuLrRZOcLW+ha3TukCVe27t/rukCkVLS0toaWnx587qthJC0kahSIiU2GhLUzNpNws22goPDxeOyCbm62WMbFicfx2RSAmdl1yFS3AU4uJiERMTw7UohAUHwMPJFs/vnsSSIdpQ4R6rqbMYr8R7SgWZoY9WWdQbsBPS3GF8+/atpF7rv//+K/QSQlKjUCRESpcvX+aXNLBgGT16NL/RsNQiXfDkygnsNFmCgdrCNlHiVqQ8mnfsjl699KCrq4uePbuja8e2aFKnEpQljyuOXmvuQxzDCcF3MKRGeTSQMhRtbGz4YgPstdq0aSP0EkJSo1AkREqHDx+WBNmiRYtkqyEa4wvbV49w49JZnDh2EucvXsKlS0ntwtmTOHL4IA4e/N0Oce919NgJnD57HhfZY6+a46P775FpVkKRlXijUCQkYxSKhEhpz549klBcu3YtEhNzbrF9ZmQNRSsrK8nl02xX4iGkAKNQJERKu3btkoSiiYmJ0Js3ZA3FV69eoWLFivy5d+jQQeglhKRGoUiIlNi+hOJQZOXe8pKsofj06VPJJKEuXboIvYSQ1CgUCZHStm3bJKHI/j8vyRqKbIsrdXV1/tz79Okj9BJCUqNQJERKyUeKW7duFXrzhqyhuH//fhQtmlR8fNq0aUIvISQ1CkVCpLRz505JKG7cuFHozSOh9zC0JheKA3fjp9CVkRUrVvDnzQqCr1+/XuglhKRGoUiIlP6W2aeJ8XGI8j4P3bIlUaXbWnyJjUNCQsbnMn78eP68lZWVcfLkSaGXEJIahSIhUjp+/LgkFNlOE2xH+9wXB/d397B3yQA00KyAyvW7YqapGT65ZbzxlL6+Pn/epUuXzubuHoQUbBSKhEjp6tWr/JZRLFzYFlIyVbSRo7iYSIQFByE4JAQhwcEIDo1AbFz6I0W2u0fHjh3582ZFwR0cHIQjhJDUKBQJkdKjR49QoUIFPly6d++e5dqnuc3JyQlNmzblz7tatWoIC5NqO2NC/i9RKBIiJVZUu06dOny4NGvWjB+B5QevX79G1apV+fPW1tYWegkhaaFQJERK7LJjixYt+HBhJdOioqKEI38HNvGH1WNlO22wc4uIiOD/vHfvXhQrVow/74EDB+abMCckL1AoEiIlHx8fvhoMCxcWMmwG6u7du/n1i5s3b+aXabDlDuvWrYORkRFWrVrFL4VYunQpX0B8wYIF/ASdWbNmYfr06ZgyZQomTZrEzwwdM2YMRo0ahREjRvA74w8ePJgPsP79+6Nfv378gvvevXujV69e/O7/Sbtp9OQv4+ro6PBbWXXt2pU/v86dO/P3EFk5N/Zn8e4YrLFSb3m+nISQvxiFIiFSYqOuQYMGSQKmcOHCKFKkCBQUFPj1f+L+v72xr0Ee8rIgOiE5hUKREBnMnj07zaBJq7GgZIEpDk9FRUW+qgzbk5GNNNmaQTabtUSJEihZsiRUVFSgqqrKt1KlSkFNTY1fQsHKs5UpUwZly5aFhoYG38qVK8fPJGUTf1hjdU3ZKJA1tsM+u7zLRojieqessXNhfcbGxsJXkzUvXrzAgwcPsHz5cly7dk3ozb7IIB+4OX/nJwY5u3khMCJBOPIXiA6C61db2Fi/xxdnH8hv3nEUfJy/4IO1NT59c0NwjNAthdjIcAQHBSOEzULmWzD3518IjYzBX/Sdy3coFAmRQfI9Ff/77z/+0ii7RMoulbJLpuzSKdtBY9OmTXzRcHZple2uYWpqin379vF7JR45cgTHjh3jF9GfPn0a586dw8WLF8E2MTYzM8P169dx69Yt3LlzB/fv38fDhw/x+PFjvqg3CyS248WbN2/4iT9sn8SPHz/C1tYW9vb2+PbtGx8qP378gJeXFz5//syPDFmwzpw5Ez9//kRsbKzw1ciOvVeTJk0k3wP2uqyEXHZeE4khsLu9C2P+awC1IkmvW7LCP+gxfhWuvPVCXqwGTS7Y6Sl2zBmC7jq66N1LFzo6/TBvx3W4RggPyKK4oG+4YDIdfbrroKdeL/TorosRhgfwzitSeEQG/C2xc/5oGOj3Rf8BAzCAbwbQ1x+PvY8c5Bja/38oFAmRgbe3NyZPnszf12MhlB+wkGRrLH/9+iX0ZI2rqyu/F6M4EMWNjXpXrlyZxQk8kfh0ahZqF+Vep0JtNG/dBs3rakJReG3lWnrY+dQTeXWhNszxOqa2rQCN5uNx6WMg1xMH+xtL0VJLE13nnIWHDCO75OJC7LFjaBOU1mqDVTc+8yHm/+EMRjbWQI3eq/HaK6MXjsGHvaNQJtnfgaSp6+KYdYDwOJIVFIqEyIjN7oyMlOK3+QKE/TLAJvT88SGcrI0bN45/nCyiHM5iYKsG0JmwETdefoKLhxecPz3D6TVDUVct6XXLtFuIV7/ihWfkoggHbB9cB4UUamDRA1+hkwmF2YIOUFKogLHHbCHzmSWE4/HGHlARlUQfEwvu14LfnC5PhoaoONrNOw+P9Abf3g8wvUcrdBwwBUuWL8FCQ0MYsrZgITadew4fGiZmC4UiISRDwcHBGDJkyB8hyBq7F8oKAoj/zGbFSl8xJwJPtszChMUH4fhHAATi8oL/UKYQ97pFa2LhXX+hP/f8MFuEf5REUGxqiA+p6jSEPTJCk1IiFKk3CRb+st3Bi3C6BAMN7uuq1AP7rVImWLTnE0yoxh1T74Qdz9Mq9R4Jq91j0Ul/EZ7TgDBHUCgSQtLFRsUzZsyQhB5bAvLvv/9K/syKGLB7ney/4j62ltPR0VF4hYy44+a5C3j+iV2W/FO8zV501SrMvWYpDD8gzevJUeIP7B3bHArc11Nv2iUEpb6x6X8Dw+uV4M6tHCaedRY6pREL6119+cvD5TrNxeMgoVsszAWHR1biXlcROkuv4I9xt+djzOzcCHrcsZ/xiXl2Wbkgo1AkhKSJXSJes2YNP3uWhV3dunX5CT1Tp07l/8xa8+bN+cfa2dnx6yRZH1sj6efnx/dnLBZRMbFISG+gFXALoxqpcK+pgemXpLgsGxsKp8+f4R6YSVGFyAB8/WQHnwxmtyY6XcWYZsrcexdC763vUlziTPIRq7pW5o83mXQGwUJvpuLcsV0/qVRgoyHb8FXolkjww/1VXVCIO15GZxleeyeLvYQIWB2ZgErcMUWVsqjWsB2GztuK2+89ECnzdNMEhP/ygbvLD/xw8UBAWNrTmRLjub+j8FAE/QpBtORUYhAc4IeAkD+v00aHBMAvIASx+TitKRQJIWliM2LFgciWfbBZsQy7dygORTYTVczFxQVLlizhg1Mu3C7AoE5xiErr4JSTFDfK/F9iSY8GaDZ0E96nN6cozhtmK3qjThMDnLBNf/qot/k2dCzLvkYNTDzjwMV3ah4wHfwP/z2o2HEJ3kkZSvFB9zG2lhL3PCV0mHkKf/7qEIwXpoOhwr6/NQfj5ocQoZ+LsUA77BzZCKVVS6Cw8P1nTVGjMcasvwrXUOlOIszTFlf3rMTEkUMwwMAAAwYPwuhZG3DPPkC4PxrPBaYHPlhcxZ71hhg3qBf6TjsAVy7o4n99wcmVY9G2QW00152Na1+EoW5iKGwum2B4p0ao20wPm+46IiafBiOFIiEkTaxmaqdOnfhlF2wJiRirvpNWKMrbrzsr0KiUCDXHnISvVLNZYvD5mhHalVdFkzG7YZd6+MaNwu6Y9EcFtRoYtfUB/DLIENuzC9GAXx5SG4vuu6QxmeYXToxvwl9eLdV4LG5JeX8vyuEQummwQg9q0F1+kzvj1MLx9vgElGffX7XOMHvuIfRzeR7ug09Pb+PKhRPYabwIY/t1RA1hMpJIVBad5pyGy+8MTUMsnJ8dwqh2dVG3TX+s2GuGd45e8LE7j+EN1VB94D748797RMPr62uYHduAwS3L8q/fYqE5wvw/Y99sA3Ro1Ry1yieVDdTbZs2N9CNgc2Ix9Ds1R8OaGvwot/qY4/DMp3PRKBQJIeny9PSUjBDFcicUA3B6ujZUy/6Lve9S33jLSDy+XluFNhqqaD5hL+zFwZjoB/PNg6CpUgVDN5lzr56ROFgemoLq/NfYBGtfeKSxGD4UpyY340dsxf8ZiAuuQncmwt9sRms+yDTQz/ix0JtcBKxPT0JF9t5K2rj66LvQn4YEf1jd2MmFnFDGT6kSJh60Qtq5GINvt9ejg0YxVO+1DE8lU1tjYH10KqpyvwCo9dkN/xRB5ordIxtzwV8Bc68+x1mjaZhgdAlffN9j+6iG3HsWhoHpG3y6uwcTxy7FzY/OMN8xChrcuVQcfhju2VzHmVcoFAkhMsmNUAx8txtdq2pCz+gBwmS+DBcL+4tL0aKMKrRnHIdToD9e7RkFrZKaMFh7K8MRYpIYvNw/EVXY11ioOTa88RT6kwvGiQlN+ZFiiX8G4aK0ofhqA1qosu9deQzY+EzoTS4Cb0+MRwX23sW4ULTIIBQFYd9uYGZnLf7vQ6XDPDzx/HP86ff+JAyqFEXheqNx2zX5/cNIvL+4HqNHTsXB524pLhMnfr+KUU2VISpngA1bDDHb+Bxc2EuHvsQiHW4EqdAYK07sx8qFa3H1C5ueG4wrS7uhGHcendc+wi8pLyn/bSgUCSEyyfFQDP6IjQOaoInBetiEZPXGVAxsLyxFu+qV0bB1K9SsXAMD1lyHj1SXYRPx9tgM1OK/Rm6k+NwjjVmevjjIj5a4EVajMbgp5eXTSJsdaFeavS43UlxvIfQmFwrLgyOhzt67VGeYPXMX+jPmZbEFHdg90GLtsN0i1XNCvsJ0RB0UEmli0lm7P7+W+GiEhf95z/bHleVoWlwEVW0DTJlrCivhGnbAsz3QKS9CoX8GY/6shTjyTPiNwPc5lnRT47622lhl/j3flpqjUCSEyCRnQ9Efd4wHo2XXybjqkMVyMRJuODy+AX+exf+djafJ199nwslsFVpwgcA+4BffS+ueojO2GtTmX1uz3QK8kTIBYj3Poa9m0jKTnstvpVGO7ReebuvLj7ZEVfvjho2Ul44jv2HPcLZetCYWXf+cLJAS4fpoM7SLcSHWYg6eeUgbVf64ulIXJbnz0GgxGPstxVOCIrlR9Dhosv5mXTFt1zMECt8cvxcHoFOGO+/aE3D/ez69dsqhUCSEyCTnQjEa704Yonu3kThsmd2V6cF4snsc6lVrAJ0+ffFvneroNvc4nKTcAjP87VH0qcEmxJTCuBNf/5wQk2iNpZ2SLlk2GHWYixDpJEa+x6I2qtzzFNF2ynH4CP0S8b64u6wD/7oqnQy5EBP6M/UL90x6oLCoLlbdTbamM8EHN9d04ye/tJ5/ER7SFpL1s8QqPVZMXhHtFl6Cn/h5UQ44MClphKyuPQV33cRVDcLx+tA4lOX6a447BKdUxQ7yEwpFQohMciYU4+Fwcz366QzC9oduQl9WheLlvgmoXqoC+qy+gQBu3GR73hBNyqij8/zTcJVidQeC32CZHluHKELH1U8Rmfqao/9NjKxfkjuuhkF77YROKSSG4+a8pEIHtfSN8D71EDTMFYdHsYkzhdFm9gmkuP2XIS4UjbqiZDl9nLVNNtUm6DN2Da7IvZ4qhpk+kXo9pb/lEeiV5/6OVXvgSLJaqjGOdzG5sSL3eioYuP3J70k9kU44MqEm16+OsQdfchGZf1EoEkJkkhOh6G6xCyN6D8Fm87RnrEQFOMLOIe3KNymFwerIVNRWK49eKy4nGxlF4N3JuWioroEeSy7APdMrsxF4sWUI1BVEUNPdljTBJJmYV1vQmt3Dq9ALF5zTvlEZFxH25wiT4/t0PeoXEUG54RBcdEx5OTPO5w3mNuJet3hjrDD7If19uUhbrOtdFy3GHYZr8hmkvjZY27MU93dVHAN3JQuxZCJ/WOH5O4dkVXsiYXl0Ij/q0xyyG1/ChG7uFxfHe2vRWFGEIjVG4vKX3wXgo77fx6Q63Hmr6eCgJbvkG4+4hPh8WXGHQpEQIhN5h6L7s70Y0r4dxm2+AUfvn3B1doYz11xcnPHdwQ5Pr+2D4eSJ2Pk4s0uqv/D62CzUVy+HnovTKqgdzgXmDNQrUwF6yy/ieybDmTiPuxjXlAsU1Q446pB8eBmPV5sGQF2kgLZL73ExnFosvtzYiOH9+mDMimN/rJdMiP6B/UNqQFS4FuacTlnTxveFMepy39cqfY3xKcXtxER+0f2j+8/h9Me0zii83T8FrVsPxNEPqX5xCPuKvSO49+JeU0t3Nd6kKmrg984Ma+cbYr+5A4LFoRj5nRv1sfulZTDu4Kvf1XziA2C+XgeK3Ci25ZxTcJMkfjy+P1qHBtwvEGX0jPHW2RXm583wwTuMQpEQUvDJLxTj4Hh3O/SqswovKqjVuCkaNaiPevXqSdo/dWqgvEoxVGxvCOvM7geGvMXK/u2gP+84XNK9RBqOZ3umol2HYTj3LbPrqNz5XTZEw1Il0HLaWfwUBoTBn85iUD1VaHZagGdpTWdN9MCO3kml3ESqrbHl5Z+r2ENsT6NvzaIo13URXnol9cX7v4ORbhWUqNkLh96mCrdof1xf0gUaZTRRv+tobD7zGA5evvD48hyH14xH1y4DsOXejz8n7iRGweroFFTl/75KoWnvadhy4BTOndyHVbPHwGDAOGy9bY+QZDkb7nAbo6tyj9fojeNvfydzgv9HGHUsApHCP1h2+VuyUWwIXu7U57/eWj1GY96ytdhy/BG8w6W+9vtXoVAkhMhEXqEYYnsd09qVRwklJZQooQxFhUIoVChVU1BAkRJaGLr7Q+ajjrgw/HRzR2BmWZcYAS9X7nHSFAxNCMWbY/PRoWEj9By3EGuXz4R+m8ZoO2QlzH+kV7IlCq/3T0YjLU00H2KEl2mW44mHx9M9GNy6Hlr2moRlq5dhrG5rNO00Goefe/xZVi4hAm8PT0SNYknfdyW1iqhdvxGatOyAAVONYPbeO93NmOPCHXB8Tk9oKQnPLVkaGhoV0bjnVBx77poqSOPh8tgELVRLou6wrfiQbIvMX18vwKBCcai3mYabTsm/piC83KKPYoULQ0WrJaaZPoJPVH4cIyYpcKEYHR0Nf39/vsXF5c/fVAj5m8krFBOiQuH70xPevr7wzaj5BSAs03uAOSkWfo4vceHgLmzdaorzD2zgnUExcV58JIIC/BEcnvGJR3p9xr3zB7B1y3YcvmgBpwyKmSdyof/d6i6O7DDB2nUm2HnoPJ5+csGviMw/5xJjg/DlxQ0c2moMo/U7cOq2FTxC0/rtIRFxUSHw8/HFr7CoFPc042PDEeDtC7/g8FQFvxMR6maFc/v24eJjbtSZzz92C0woxsfH49mzZ5gzZw5fpZ/VbFy8eDFevXolPIIQIg85MdGGkL9FgQnFzZs38xuein9Yxa1UqVLYv3+/8ChCSHZNmTJF8vPF9k4kpCD5q0Lx8ePHWL58ucxt8uTJKF68eIowTN5UVFQwc+bMNJ9LjRo12Vrjxo0lP1vly5dP8zHU8rZ5eQmzd4jM/qpQZHuxJQ8zatSoUaMme7OyshI+VYms/qpQXLVqVZp/wdSoUaNGTfr27t074VOVyOqvCsWdO3eicuXKMjW2ASqbup3WP4zkjT1GQ0MjzdegRo2a9K1EiRKSnytFRcU0H0Mtb5udnQyl50gKf1UosiUUbEmFLO3BgweoWJHV9vszCJM3du/j8+fPab4GNWrUpG8jR46U/Fyx+4tpPYZa3rbExPy7TjCv/VWhmBVhYWHQ0dFJEYBpNT09PeEZhJDsGDdunOTnqmnTpkIvIQVDvg9F5uLFi1BVZdux/BmGrLFLrObm5sKjCSHZQesUSUFWIEKRXSrYt28ff88weRiyVqFCBZw8eVJ4JCEkuygUSUFWIEJRjE1DZjNY9fX10bt3bxgbG8Pa2lo4SgiRBwpFUpAVqFBkEhISEBQUxDdCiPxRKJKCrMCFIiEkZ1EokoKs4IVibAC+Wlng2sUzOH7kIPYfOILz1x7i/Xdf6XexJoSki0KRFGQFKBQj8cXiBJaMG4g+/Qdj5LhJmDp1KiaNHoiOTWqiesMemL/nLlwy2W2bEJIxCkVSkBWMUAz8hGNLB6J+leroOt4YN9+6pNg408/+Bmb/q879EGtAf/U1uP+xgychRFoUiqQgy/ehGPn9Adb0rwclkTr6Gt2AdzqBF2i1A21Kcj/IxZtjzW0noZcQIisKRVKQ5etQjHV9hGW9KqOQqDD+W3oF3hndNIz4gW29y3M/yIXQcIwpvkUK/YQQmVAokoIs/4ZihCMOTWoJBe4HU11nKV77CP3pifPHTcPW/A9y4cZjcetrjHCAECILCkVSkOXTUIzD+5NTUaMQ94NZrDGWmjlmPrOUC8U7i9om/TBX7IWzr/yFA4QQWVAokoIsX4ZinKcFpjZJ2r6mcl8jvAsUDmQk0hOnJtRL+mGurI/zlgHCAUKILDILRQ8PD+H/CMl/8mEoxsN67wCosR9KxaqYfMAqxUzT9MQH2mFV56Si4YpNx+PWF7p8SkhWZBSKZmZm6NSpE06dOiX0EJK/5LtQTIz8hBUdkgp/K9cbhNO20oVbqOMZ9C6X9INcY6AJbEKFA4SQDL18+RKbNm1CZGTS7LT0QvHevXv8vqWsnxXnf/z4sXCEkPwj34VixMfdaFc2aaf9egM3wDZOOJChBHw9OQYa/A+yBgZtNEeYcIQQkj4LCwtUq1YNhQsXxvTp0/m+SZMmSUKxWbNmfN+jR49QpUoVSX+HDh3w48cP/hgh+Um+C0WPc1NQsSj7wVOD7rLr0oVbrCt2GlTlf1gLVdXFgTchwgFCSEZ27NghCTrWZs+eDV1dXcmfW7VqxY8k69atK+lr3749nJxoLTDJn/JdKH7YOQBl2Q+fQjWMNn0n9GYs+M0maJdmo8siaDPlGFyFfkJIxqKiorB9+/YUm3grKChI/r906dJo1KiR5M/a2tqwt7cXnk1I/pPvQtF29yCUYT+ASnUw/fgXoTcDCV44NKYhFLnnKHKjxMPvaZRIiKxOnDjBb9gtDr+0GruUamtrKzyDkPwp34Wi/52FqMkunxauirF7M99A2OXaQjRQZY8vj+E7X4Dm1xCSNTdv3kSNGjXSDMQGDRrgw4cPwiMJyb/yXSgm+DzA2H8UuR/EYug4+wwyWm0YYncRwxuocI8tDu1pR/GDSrsRki3Pnj1Dw4YN/whEa+vMf0ElJD/Id6EIRODZpj5Q5X4YFesNwtl0yrWF2F3HjLZluB/akug0/QA+B9FuioTIw7t37zBx4kTs37+fn5HKJtoQUlDkw1AEEgM/YOvwRiiioIDafVbC3CEAwWHhCA8LQaCfB15fMEH/pppQq9QKs/c+hFeU8ERC8rnExEQkJCTwLT4+HnFxcXyLjY1FTEwM36Kjo/nGJsmwtYURERF8Cw/nfka4FhYWhtDQUAQHB/OPzwr2egx7D0IKknwZikxCkD3OrByGFrVrokE7PYyZYYglhrMxZqAuOnbsjrHLDuD591+IFx5PSE5gwfL161d8+/aN/y+befn582fY2dnxk04+fvzIX1p88+YNP6J6+vQpv6bv/v37uHXrFq5fv44rV67gwoULOHPmDD+h5ciRIzhw4AD27NmDnTt3YuvWrdi4cSOMjY2xZs0arFixAkuWLIGhoSHmzp2LmTNn8htqs9Hb2LFjMXLkSAwbNgwDBw5E37590bt3b/Ts2RPdunVD586d+SUTbdq0Qb169fj3JoT8lm9DUSzC5xue3rqEU8dP4MwFM1i8+QK/CLpUSnIeG2UtX74cJUuWhIqKCooXLw4lJSV+oXvye25/czM1NRW+GkIIk+9DkZC8EhISgkGDBqUZNrnVChUqhCJFiqBo0aJ8KLOALlWqFNTV1VG2bFm+7FrFihVRuXJlvjJNrVq1+IX2mpqa/GMvXbokfDWEEIZCkZAs+vXrF/T09PhwUlZW5i9L9u/fn28sLIcOHcpfymS1QsePH4/Jkydj2rRp/OXOOXPmYMGCBVi8eDGWLVuGlStX8pdG2SXSDRs2YPPmzdi2bRt/+ZSN5vbt28dfUj18+DCOHTuGkydP4vTp0zh37hwuXrzIXwa9du0abty4gdu3b/N1SB88eMCXaXvy5AlevHiBV69ewcrKin88C0o2umWvRQj5jUKRkCxydXWVFMBmVV1ev37NByVr7F4jm8zCJrawyS5s4gubEMMmx+Q1NntUPNJkdUxpsgwhv1EoEpJFbM0eu3zJwoWNClnw5Qc2Njb8KJGdN6tj6uPjIxwhhFAoEpJFbFaoeMTFLn3mFw4ODqhduzZ/3i1atKDdLAhJhkKRkCxgM0+HDx/OB4uioiJ/by+/cHNz4wt3s3NnE2++fJGihjAh/ycoFAnJArZ4/d9//+WDhe0jyCay5Bfe3t7Q0dHhz53dE6WapYT8RqFISBaw5RhsmQMLlqZNm/IL9/MLNhGILexn516sWDG+sAAhJAmFIiFZ4OLiwq8HZMHStWtXBAYGCkf+fmxG7IQJE/hzZ41V2SGEJKFQJCQLnj9/zi9+Z6EyYMAAvhZpfsHuh86aNUsSimw9IyEkCYUiIVnAJtawkm4sVFjN0WxLiEWInxfc3Nzh5e2HgIAASfPz9oK7myvcf/ojLCr76xxZ8XBWM1UcimyhPyEkCYUiIVnAKs4oKCjwocIKdGdXQpQPLI6sw4IZo9C7szaaNmvG72TftHFDNGvbEyMnzYThxuN45RQsPCPrWBGB+fPnS0Lxzp07whFCCIUiIVkwe/ZsPlBY8W+2m4XcxLjgxJyOUBICS1RYEwONb8AlXDguBzRSJCR9FIqEZIGBgQEfKGpqarh69arQKw8xeL53LLSEwNLquRGOWdvyMF3sniKrvyoOxYcPHwpHCCEUin+zxHB4OTvC+WcQpJrGkRAGzx/f4Rkk509R8ge2LyELFFZYmxXclpsEV5ye1x5F+cBSxcB97xEnHJIXVuuUFSYXh+Ljx4+FI4QQCsW/UhTsrm/DmO6t0aheHdRt2Az/DV+O67YBwvHUYuFwfy+mDR+KcZMnY8ywoZi97TrcKBtzDNsRgwUKW7jPNg+WG6+nWNRFLSmwVDpgz3t/4YD8sMIDtCSDkLRRKP5tEmNgf8UIvdu2Qlf9IRg1WBcNNJKKTpfrYoiHPyKFB4olwP7SUrSt1RBjtt7CN6fvsH+4DwOb10b3RefgLu9hRgGXmJgo/F/GxGXS2B6FlpaWQm/2eT0zRRf1pLBSab8MNv7y/wtkM1rFl3/ZHoy0eJ+Q3ygU/zKxbubYsHQljj12QkR0HOJio+FleRSD/1HkPsTKYMJJG0QIj2Vivl3H6AYKUO++HnahQif3iKdb+6KEqA7mX/os98tvBVlYWBg+ffqE79+/8/+fnubNm/OhUqNGDVhbWwu92RWCZ3uGowz3uiKRAtovv40cyES4u7tLStRVrVoVnz9/Fo4QQigUs4BVBLG3t8+R3QVCftjD7rsHUu5w5w+zFd1QmPsQ673zGffRKUgIwsPNfVBSpIRB+14h+QTFX2+PoUcpEReW67jRRt7v4ZdfsEuLY8eO5XetZxsEs5ml7J4hC0k2a1NMHIo1a9bE+/fvhd5sCnHC3uHV+dcVFamP5bcdcuQXmm/fvqF69aT3YSNeVp2HEJKEQlEK7JIa+yC5efMmv13QqFGj0KZNG36X89wRhvsb9FBcqSGMH7tLPigTfN5i1X8qEBVuCmNzJ6S48Of2GPPbFoVIuQP2vf6Z8hjJ0N27dyX7DbJWpEgRtGzZkp+cwna/ZxNTGjRowB9ju0zY2dkJz8yeUMebGFE96T0V60/A7W/JrwnID9tPkdU8Ze+jr68PPz8/4QghhEIxHc7OzjAzM4ORkRG/RRAbGZQoUULyQdmzZ8/c27E8wg6bR7ZDl6mn4J5sOBhocxZ9ynDnU7YXTlimmpARZIONAypx56qG8afepbjkmrlYOL++im0rF2DunHkwXGaCc8+cwLbQjfFzguXDm7hwcj82bt6Jy6+9+We4W17CesPZWLbdDE5hQgSHOePe4XWYt8AIV218kV/Gq2yz4CFDhkj+rlM3trMEuxfH/r9MmTI4dOiQHDYYjoPjTUPULJT0Hg3GH4BDDv3zYqEu/lpYNZ7IyNT3qQn5/0WhKGDb6bCRIKtO0qdPH76aiLq6uuTDI3ljo4hc2yoo3g+PtoxH977zcd87+XgvEU6P1qEpO6e6I3HNNlXsRdph9+h6/Pl2W/cIAdIOFX/Z4ujiIfiv+wDMMzmIs+cuwHTpIDRrOwyXbMMQF+SC17d2oF8tJYhUG8LI3BOOd3djTLeGKMXOpUhtGL3gPs0DbXFs2VA0q6zKn0O9qRfhn49mw5qbm6NcuXIp/t7Ta5qamujSpQumTp2KY8eOZW3HjNgA3FyoDQX+NStgwsFXyKmoYiXqxOfO/r1LO7mIkP8H/5ehyBYv+/r68h98q1atQo8ePVCnTp10QzB5K1SoEF/NJMcl/ML7m4dgOLQdNBRFUFCphJ5z98HGTzzeisXnW4aowc6rxRTccUx19ynmC/aOa8yfs/aiO/D5fTssfb6WWD+oMaq0GIFDj38I9yh/4fzUulAq1wn7ngfxPYmhLzG5rio0W43GoZtnsW7JOlx5a4ltgxughHJlLLhog5u7l2HlgYd4dmoJWpQWodzAQ/iZauTDRldsMsvf2IKCgvh/F6n//jNr7GoCm5Hatm1bzJs3D9euXcPPnz8zHUnGBlpjUZukAuOiiro49Dq95TfZt23bNsn5mpqaCr2EEOb/IhTZ3nceHh78hIn169dDV1cXWlpa/C4H4vqV0jb2HHYvkV1eZRNt5NXYB2cK8YH49PAKTFdNhZ52TSjzl9WKoeOiK/DkR1xxsLs2F1W5cyrUahruOaVa3h/1GaZjku57aS++C9/MZmzEeeD8rFYoqt4G6x+4C52cCC/c2j4PS0zvwD0maUQRbWuKdlrl8U+niTDZtBFXPrExjQOMetZCqXJdsGLfJhjvNccv7pS+n5uL2lyot1/zFKGpTnHGjBn8pci/sbFF+eJLpNlpLCQrVKiA7t27w9jYmP83yGZ/smURyS+/B77fiTYlk56jpbcMr3IoE1PvkMFGjYSQ3wpcKLIPGi8vL9ja2vIjQVa4ma3JqlSpkswBmFZjI8WiRYvyNS/l2dhO6OlJDP2GMwu6o3QR7hzK9cX5b0lLBRzuLcc/7LyaTMSdb6mGgmEfsX1oLf6cdYwtEJBhSZwEeDw2RqNCRaA96zRSxfMfbE0HopxKUdTWn4cTD535vvhPB9GjVgmUaDgQS9Ydhx0/zPyJ4zPbQElUAysfuf5xT1G8Vu7/rbHQZZN22L292Lik78r7nf2gwh9Xhe6yK8ipcSLbYJiNYtl5sPuhcq3GQ0gBUKBCkd0bYWHILonWrl07xQfR3946dOggfBXp8H2MOR1Lc4+tjZXPvPguH8sD6FKMe36NYbj6SbJIMYn/Gxj1ZvfESmP8SeuM70/FeOPs+KoQqbSC8V0foTM93tgzqA4URMXRc8Vt+Aq9docmoyZ3LmW0x+CEjbC+7+dDzGqrAlHVsXjo+ucZ9O/fP8X3oCA3ZWVlfsZqr169+B0qTp8+za8PjI3nQjHRC7sMqqEQe6xqcyy74ip8h+TPyckJqqpJ93nbtWsHV9ecey9C8qMCF4pswsyzZ8/4GYELFy5E7969+QXKqT+k/rbGlnhkLBAXFnRGCVEtrH7pyffEulhgVrPCECl3wt5nHnyfWKLzQ8xsXQQipbbY/dIjwyUZMT4vMLGGCEqNh+Pyd6EzPd5XMKBWSRSu0B0nHMQzZ37iyOQ2KCoqhNbzr+GX0Ov9cCvalRSh8tgTcE1jJiW7DL127dq/sm3YsAENGzZM8+9K2lavXj1+FiubwXzx4kV+bWtak1riPS7CoIYy/xzVFqNh5iYcyERMZLTMk2TYPU7x+Y0bNy7F2ktCyP/BPUV278bKygoXLlzAsmXL+Hs7pUuzEdefH2LSNBawBw8exJkzZ+TaLCwshDNOTyiuLuyMsloGuPZdWJcR44kLhq24EUZZTDltwy+ZEPv17gR0S4ug0nEFLL0zvqEY6noeulx4qbSagNt/XDuNxS/vH/jhlZRq3lfmobaKCLVHn5GEH3zuYkobbvSh0g6HP4n3+wuDxfaBKMmNVMeefI/8VoaV3Ydu1apVmv8G0mvs38bAgQNhYmKC69ev85Vx2KSdzHhemonqyuw1lNByzF64SpFz/lYnsO20FaJkWN3PAnTx4sWS8924caNwhBAi9n8x0SY5Hx8f/sPqypUrMDQ05O+vsMkQ7F5h8g+49FqpUqXkV8EkDYkJCfwmsH/cAvz5ADM7NYDOkmvwk/xynwj/l/vQpRz3gTz6CFwkyROLt4dHobRIE2MOWyE6kw/ZSM+7GKHFfX3q/2L93aRRKC8+Ct9fnMfWrUdhHcA+fUNxZV4nlFIoi+nXf0/G8bm/Ef+WEkFz4EFIrpKGfcHOIZW51+yJoy9tYfXgCRx+5cxi9JzAfoHK6B508mN169blR4JsKQa7ZyebcFyZ9S+Ks9dSqoYxez9mXmghyh7bhvfC3HO/S/hFBbjDzvoNPjp5IzKdBaHs3xVbOsLOmf1imHvFJwjJP/7vQjE5dumIjSRZtZqzZ8/ykx+aNGnCT0BQUlKSfOilboMHD+Y/YHLCt2vroNesAbpPXI+b777Dw8Mdrl+fYte03tAZZYyX3qk+8RKCcM+kPypV0IbRdTsEch/K3u+vYFKbqmg8bCs+pZ7ymYbESC+cndqYv6dVvNZ/mGNyECeP7sHqeRMxaupa3LIL4Ed6iUEWmNy8JERlB+LuT2FcmhiEG6t0UFhUHGNOf5KMVmOdzDG+Dvf9qtwds+Yb4eANKwTEZH4ufwN2r48t0Un+dy6eRcpChV1evXz5MipX5kKfO8Yus7IycFkS/hwz/y3Pv07Rqv/B1CadRJNIxPtD49C49Vjc8+L+DSaE4NXh+ejSqAaqaJVHGfUKaDVwKW4Lk7GSY78Qsq+BvVfTpk2zfs6EFGD/16GYWgI3SmOzV1nZLnaJdMyYMfwifjZzlc04FX9Asv9//fq18Cz5cry1EXr1tFBOoxwq12mOrnp9YNB/KGZtvIgvgemMIWLdYWYyAT17D8e8hQsxcbA+hi06iPf+0t9vCnd+iJWDtFGtYjloaFZGrfptMMxwLyw9fk+Qif9yFTP7aKP74mtcwAmdsc64sLI/WnaaiTuO4kunQIzbcyzuXhmVa7XEtN0P4C0s5/jbsfWEbJTIQpCVcGP7JrJ70+xenKenJ7+kgWH/VliJNPbvgU1cyeqoK+jBarQoy/5dFUKl9guQ8X4V0XB9sBU9qxdHkxlXuXF7PFzNN0CvbVeMXmiCnVtXY+x/tfm9GCt3WYQXqaYc37lzR7LMhBWokPV+JCH/DygUM8E+JNnWQDt37uRrnrIZe6zSyfjx43NokkICgt3t8dz8Fq7fuIVHrz7BK1i6UWmAkzUe3XuItw4+WSskHRcMx7ePcc/8CT44B0q3sXG6ouD11RpWdm6pipv/3QIDA/lJWkePHs1wJMUCZeXKlZJflLZv3y4ckUHiTxwc31JYilEImm2m475POOK5wI2Pj0N8XBxiosIR5O8Jhw+vcGXXbLSrpAiRQh2seeyFhChvXDZZiP2WyWqXhtrCWFcLIqVKmHIm5cxS8fpEdqtgyZIlQi8hJDkKRRmxy6337t3jL7dmv94lyc+uXr0qCUVWiCCeLa/ITHwEXN7ewYmDu7BybAeoCc9PatxosbkODAb0h4FBPxj06wt9ve7o1KYJqpRKds+7yRy88I5FfEwIvry3/2O5jfupUVBRqQCDre+EnqT1iY0bJ1U4Yr/UZT6xi5D/TxSKhGQRu/co3m2ClYRj9+wyFR8Jjw8WuHTmKEx3bseuvfv5nTf4tm8Pdm7dzM8KlbRNm7B5yzbs2GWKvfuTHnfhmQNCM7gU8PPCZGhpNoThzd8jSDb7mlVjYufasWPH3CtmT0g+Q6FISBax0nyNGjXig4btT8i2ZMp70bizqAvq/jcfbyQbbwKjR4/mz5Ntg8XKzRFC0kahSEgWsc2m2X1mFjZsicalS5eEI3kn3v0axnXqjEVXHCVLOxwcHCT7P7JLp6yIACEkbRSKhGQDm6XMwoY1titGnlaIifPF5eVDMHTFRaFofBJ2yVVRUZE/R1YMn82cJYSkjUKRkGywtraGmpoaHzjsUirbASNvhOHDuZUYP2cXrJPtE8aWkAwbNkwS3Gy/R0JI+igUCckGtoSjb9++ktB5+PChcCQ3xcDpoSlmz9mEx99TFoa3fPWS3waLnRvbnYMKgBOSMQpFQrJpy5YtklBkC/9zqtpR2hLgankWK5dsxmO3lIszApytMXTsHMm5sXWKVACckIxRKBKSTWzNn7q6Oh88zZs3z0L906yKh8vTPTBoVR/tB83Fpp1bsMFkA9fWYsWCmdDt3A/FSieNEtn5vX37VngeISQ9FIqEZBPbrqxr1658+LAJLWzrstwQ/PUqJrTWQgnl4iitUQ7qaqVQqpQa1EqpQlW9EkQaSZsJszZ9+nQaJRIiBQpFQuRg+fLlkp1WJkyYIPTmrPioYPx0c4Onlxc8Pdz5ST6seXh44v6DR1wwavDnwwrcv3z5UngWISQjFIqEyMGbN29QpUoVPoTYhJa83oFi6dIlSTv5c23KlClUwYYQKVEoEiIHrEC4eOlD4cKFsWrVKuFI7vvy5Qu/SJ+dC7uX+PjxY+EIISQzFIqEyImZmRlUVFT4MGJbjrHi8bmNhfPYsWP5c2CNlXejwvWESI9CkRA5iYiIQIcOHfgwYptUHzlyRDiSe1jhb3GRcrah8PPnz4UjhBBpUCgSIke7du2SlFTr2bMnH5S5hS3Mb9GiBf/ebNLP0qVLaSNhQmREoUiIHLHto9iO/SyYlJWVcerUKeFIzmL1TOfM+b1QX1tbG/7+/sJRQoi0KBQJkbPkFW7Y3oW+vr7CkZxz+/ZtlC1bln9Ptm/inTt3hCOEEFlQKBIiZ35+fmjatKkkGPft2yccyRlsRNipUyfJ+7ERI+2EQUjWUCgSkgPOnDkjWczfsGFDODs7C0fki1WpYfcOxYGYtzt1EJL/USgSkgOCg4P5iTbisGK73efE6O3kyZP85VL2HkWLFv0rNjomJD+jUCQkh9y6dQvFixfnA4tVubGxsRGOyAersaqpqSkJ3rlz5/L7JxJCso5CkZAcwhbNjxo1ShJavXr1Qmhoyv0Os8rR0THFfct+/frl4u4chBRcFIqE5KB3795Jlmiwe4wbN24UjmRdUFAQ9PT0JIHYqlUr2NvbC0cJIdlBoUhIDjtw4AB/v48FGKtJmp0qM2z0ybaBEgeilpYWHj16JBwlhGQXhSIhOYwF2YgRIyRBxpZPsGUbsmIzTdmEHVYUgL0OK+d2/Phx4SghRB4oFAnJBeweYN26dfkwY7toLFmyRDgiHRaIJiYmKFGihCRcV69eLRwlhMgLhSIhueTcuXOSy6iqqqo4ffq0cCRjbEapkZGRZITI2rRp0xAZGSk8ghAiLxSKhOQStk5x9uzZkmDT0NDAgwcPhKNpY4HIdvUXhylrs2bNQnh4uPAIQog8USgSkovYvcQ+ffpIAq5+/fr48OGDcDQldi9y0aJF/OVW9lgFBQXMnz+fRoiE5CAKRUJy2bdv3/hlFOJg7NKlyx+l2diyC7YYnwUhewwLxoULFyIqKkp4BCEkJ1AoEpIHrKysUKVKFUkwDh8+XLKw38XFBcOGDZMcE0/MoWo1hOQ8CkVC8siNGzf4+4ri8Js5cyZfGq59+/YpAnHlypUUiITkEgpFQvLQ3r17JfVRWcUb8Z6IrJUpUwa7d+9GXFyc8GhCSE6jUCQkD7HA27x5M5SUlCRhyFqDBg34jYMJIbmLQpGQPBYfH88HI6tQwwKRLfLPTik4QkjWUSgS8hdgwXjkyBHo6+vTnoiE5CEKRUIIIURAoUgIIYQIKBQJIYQQAYUiIYQQIqBQJIQQQnjA/wDYkgl/FHvmrwAAAABJRU5ErkJggg==)
physics-General
physics-
Figure shows an arrangement of an equiconvex lens ( f=20 cm in air) and a concave mirror (R=80 cm). A point object ' O ' is placed on the principal axis at a distance 40 cm from the lens such that the final image is also formed at the position of object. Find d.
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)
Figure shows an arrangement of an equiconvex lens ( f=20 cm in air) and a concave mirror (R=80 cm). A point object ' O ' is placed on the principal axis at a distance 40 cm from the lens such that the final image is also formed at the position of object. Find d.
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)
physics-General
physics-
A thin biconvex lens of refractive index
is placed an a horizontal plane mirror as shown in mirror. The space between the lens and the mirror is filled with water of refractive index
. It is found that when a point object is placed
above the lens on its principal axis, the object coincides with its Onn image. On repeating with another liquid, the object and the image again coincide at a distance of
from the lens. Calculate refractive index of the liquid.
![](data:image/png;base64,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)
A thin biconvex lens of refractive index
is placed an a horizontal plane mirror as shown in mirror. The space between the lens and the mirror is filled with water of refractive index
. It is found that when a point object is placed
above the lens on its principal axis, the object coincides with its Onn image. On repeating with another liquid, the object and the image again coincide at a distance of
from the lens. Calculate refractive index of the liquid.
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)
physics-General
physics-
An object is placed at a distance of
from a thin plano convex lens of focal length
. The plane surface of lens is now silvered. What is the position of image?
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)
An object is placed at a distance of
from a thin plano convex lens of focal length
. The plane surface of lens is now silvered. What is the position of image?
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)
physics-General
physics-
A glass slab of thickness 3 cm and refractive index 1.5 is placed 12 cm from concave lens of focal length 20 cm. A convex lens of focal length 10 cm is placed on the same axis at a distance of 5 cm from the concave lens. An object is located 6 cm in front of glass slab and an observer looks it from the other end of optical train. Where will the object appear to be? What is the magnification of the object?
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)
A glass slab of thickness 3 cm and refractive index 1.5 is placed 12 cm from concave lens of focal length 20 cm. A convex lens of focal length 10 cm is placed on the same axis at a distance of 5 cm from the concave lens. An object is located 6 cm in front of glass slab and an observer looks it from the other end of optical train. Where will the object appear to be? What is the magnification of the object?
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)
physics-General
physics-
A converging lens
of focal length 20 cm is separated by 8 cm from a diverging lens
of focal length 30 cm. A parallel beam of light falls on
after passing through
is focused at point
. Calculate V. Repeat the calculation for the case when the parallel beam first falls on
.
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)
A converging lens
of focal length 20 cm is separated by 8 cm from a diverging lens
of focal length 30 cm. A parallel beam of light falls on
after passing through
is focused at point
. Calculate V. Repeat the calculation for the case when the parallel beam first falls on
.
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)
physics-General
physics-
A thin plano convex lens is split into two halves. One of the haves is shifted along the optical axis. The separation between object and image planes is 1.8 m. The magnification of the image formed by one half of lens is 2. Find the focal length of the lens and separation between the halves.
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)
A thin plano convex lens is split into two halves. One of the haves is shifted along the optical axis. The separation between object and image planes is 1.8 m. The magnification of the image formed by one half of lens is 2. Find the focal length of the lens and separation between the halves.
![](data:image/png;base64,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)
physics-General
physics-
A point object 'O' approaches a biconvex lens of focal length 40 cm along its optic axis with a speed of
while the later recedes away from the former with a speed of 4 cm/s. Find the speed and direction of motion of the image when the abject is at a distance of 60 cm from the lens.
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)
A point object 'O' approaches a biconvex lens of focal length 40 cm along its optic axis with a speed of
while the later recedes away from the former with a speed of 4 cm/s. Find the speed and direction of motion of the image when the abject is at a distance of 60 cm from the lens.
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)
physics-General
physics-
A convex lens of focal length 24 cm in air is surrounded by different mediums as shown in the fig. A point object 0 is placed along the principle axis at a distance 30 cm from the lens. Find the number and position of the images formed.
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)
A convex lens of focal length 24 cm in air is surrounded by different mediums as shown in the fig. A point object 0 is placed along the principle axis at a distance 30 cm from the lens. Find the number and position of the images formed.
![](data:image/png;base64,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)
physics-General