Physics-
General
Easy
Question
A small fish 0.4 m below the surface of a lake, is viewed through a simple converging lens of focal length 3 m. The lens is kept at 0.2 m above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at ![open parentheses mu subscript w a t e r end subscript equals fraction numerator 4 over denominator 3 end fraction close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
- A distance of 0.2 m from the water surface
- A distance of 0.6 m from the water surface
- A distance of 0.3 m from the water surface
- The same location of fish
The correct answer is: The same location of fish
Apparent distance of fish from lens ![u equals 0.2 plus fraction numerator h over denominator mu end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFcAAAAmCAYAAACxtgcIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAktJREFUeNrtmr9LQlEUxx8iIiFBRDQ0BCER7SHi5CIRERE0SINEe7Q1NPQfREQEESFNgURENLRISDS0RaP/QLRIRISEUOfA94E83vX9uO/6lM4HvohH1MfX+86551wtSwjCNykhNkRPlvQqNphhlXQpNphhn7RLGicdkN5JLdK2WKNPDQY/klaQe6dIbdKI2KNHk3RHyjjiLaxmISS8Sr9cVmgSOwhBgxyp7hLPkx7EHj3KpGqAuBCAI9KmIr4l9uhxTVoKEI+dUdIJ6Rk6RUxFgXRF+iT9kF5IG326Vt4RpAPEY6eO/aLNsqJo2DSQ4+yt0DzpCTGhi3XkKyeHAc2aDtjv/8bd3vmN68C3d8klXsRrQWgPg7k1DCf8xu2L9ZIqh6Vc4in07H7JIzUMvLlN9Mp+4zp0erz24/Mz0iiEhUE3N6Fo4xKG2ruO5m0+RrpRpJYo7iy/7/X1mTlFG5fzaO/CXvy7Ii2kfaSFGRibDfGjxrJyVW1cxVB7x0Vr0SVe8ihoc6QzK/yILxZzeQvkHPoukN4MtXdrMMlJtcdWbBLFNanxvbGYy9utC+TYCTw/NtzecbrZgVmcIvbQKLilHeYOK9caNnO5QNyjUjfQLZlu7/g7z1HAvtH+ZnqYG6YoCYIgCMNJP2cv/44wsxdhAGcv/wrVjEWO1iNANWORo/UIKKODdbJpydG6Nnwk5Zy98PkfH5bK0bom1xgP8ChgFquVW/dba0CP1oeJFnJrG4/Frrj8w1EDnth9iA1mWEJaEAxQsdz/Y+HJH/7WrFvx0xJeAAAAknRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT51PC9taT48bW8+PTwvbW8+PG1uPjAuMjwvbW4+PG1vPis8L21vPjxtZnJhYz48bWk+aDwvbWk+PG1pPiYjeDNCQzs8L21pPjwvbWZyYWM+PC9tYXRoPr9/Tt0AAAAASUVORK5CYII=)
![equals 0.2 plus fraction numerator 0.4 over denominator 4 divided by 3 end fraction equals 0.5 m](data:image/png;base64,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)
From ![fraction numerator 1 over denominator f end fraction equals fraction numerator 1 over denominator v end fraction minus fraction numerator 1 over denominator u end fraction rightwards double arrow fraction numerator 1 over denominator left parenthesis plus 3 right parenthesis end fraction equals fraction numerator 1 over denominator v end fraction minus fraction numerator 1 over denominator left parenthesis negative 0.5 right parenthesis end fraction v equals negative 0.6 m](data:image/png;base64,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)
The image of the fish is still where the fish is 0.4 m below the water surface
Related Questions to study
Physics-
In a thin spherical fish bowl of radius 10 cm filled with water of refractive index 4/3 there is a small fish at a distance of 4 cm from the centre C as shown in figure. Where will the image of fish appears, if seen from E
![](data:image/png;base64,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)
In a thin spherical fish bowl of radius 10 cm filled with water of refractive index 4/3 there is a small fish at a distance of 4 cm from the centre C as shown in figure. Where will the image of fish appears, if seen from E
![](data:image/png;base64,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)
Physics-General
Physics-
An object is placed at a point distant x from the focus of a convex lens and its image is formed at I as shown in the figure. The distances x, x' satisfy the relation
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)
An object is placed at a point distant x from the focus of a convex lens and its image is formed at I as shown in the figure. The distances x, x' satisfy the relation
![](data:image/png;base64,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)
Physics-General
Physics-
Three lenses L1, L2, L3 are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens L1, emerging L3 as a convergent beam such that it converges at the focus of L3. Distance between L1 and L2 will be
![](data:image/png;base64,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)
Three lenses L1, L2, L3 are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens L1, emerging L3 as a convergent beam such that it converges at the focus of L3. Distance between L1 and L2 will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALgAAAB+CAYAAACXgttuAAAgAElEQVR4nO2de2xT5/nHv8exncSObSBxnMQOIXFICIHcKAkJ0JQCpRcCtGsZ69r1pnVtp4lqW1VVqzS12qR2qkCjXQtME2s3tFINCguEEShpSsjFXJKQMC5xro7jgJP4fvexf38wn1+S5nIcH8fY80d61ebInPO853zPc573fZ/3fQmv1+tFlCgRCivUBkSJEkyiAo8S0UQFHiWiiQo8SkQTFXiUiCYq8CgRTVTgQWT37t04fPhwqM0IOW1tbXjnnXegUCjm/dqMCPz06dP4zW9+g66uLiZOFzHU19dDKpWG2oyQo9FooFarsWDBgnm/NiMC7+vrg81mQ0JCAhOniwiMRiMMBgPy8/NDbUpIIUkSer0efD4faWlp8379gAXucDgwNjaGlJQULFq0iAmbIoLz588jJycHYrE41KaEFKPRiL6+PmRmZobEAQYs8Dt37kCn02Hx4sWIjY1lwqaI4NKlSygqKqL+ttlsuHz5Mo4dOwalUgmSJENo3fxhsVgwOjqKjIwM6pher8d3332H6upqjIyMBPX6AQt8bGwMXq8XqampE453d3fjq6++CvT0YUtTUxMKCwupv+12OywWCywWC44ePQqTyRRC6+YPk8kErVaLxYsXU8eMRiMIgoDL5cLnn38e1OsHLPC7d+/CYrFM+BRrtVq0tLTgo48+CvT0YYlWq4VCocDKlSupYwkJCSgrK8PmzZuh1WrhdDpDaOH84PF4MDAwgJGREchkMup4cnIyUlJS4Ha74fF4gmpDQAJ3OBzo7u6Gx+OBRCKhjotEImzevBnDw8MBGxiODA4OwmKx4Ec/+hFKSkqwbds21NfXIy4uDmfPnsXq1ashEAhCbWbQcbvdUKvVaGhowBNPPIGSkhK8/vrr0Gq16OjowPXr12E2m4NqAxFIuqzRaMTevXvxwQcfgMfjgSAIbN26FX/84x8hFAqRkZGBgYEBJu0NC9xuNwwGA/V3TEwMeDweamtrYbfbsWnTppB0mYUCX2jmg8PhgM/nw+12gyRJPPLII2hoaAja9QMS+HR4vV64XC7I5XL09vaCzWYzfYmw4/r163j//feh0WiwaNEiHDx4EMnJyaE2KyQoFAocP34cVqsVeXl5+NnPfha0awVF4ENDQ6ipqcGf//xnvPvuu6iqqmL6ElGi0CIoAo8S5X4hmosSJaKJCjxKRBMVeJSIhtHujb/85S+w2+146aWXwOPxmDx1lChzgjEPrtFocPr0abz33nvo7u5m6rRRIox9+/bh/fffnzBOEEwY60U5dOgQGhsbYbfbIRKJ8MknnzBx2nnHZ384UFNTg40bN4baDNqo1Wrs3r0bNTU1qKurQ2lpKQiCCOo1GQlRlEolGhoaUFJSguXLl+PVV1+FQqFAaWkpE6efVzgcDj755BN8+eWX+PnPf37fDcaMjIzgyy+/RFZWFgoKCkJtDm1IksTp06chFovxwgsv4ODBgygqKgp6BmrAIYrT6UR9fT1iY2Mhl8shEAjw8ssv4/33358wRBsuxMTEYNeuXdi8eTNqampgNpsRExMT8sJisWAymVBXV4e0tDS8+uqrYZVr3tXVBYVCgfz8fOzatQvt7e2oq6sL+nUDFnhXVxeuXr2KFStWQCKRICYmBlu2bMHo6Ciqq6uZsHHeEQgEeOGFF5CamopvvvnmvhC50+lES0sLAOCnP/0plixZEuK7RB+bzYYLFy6Ay+Vi6dKl4PP5eOGFF7Bnzx7odLqgXjsggVssFjQ3N4PFYiE/Px8sFgssFgsxMTF47bXXcPjwYQwNDTFl67ySmpqK5557Dg6HA42NjXA4HFT95rt4vV5cvXoVarUaL7/8MvLy8kJ9e/xCqVRSTjA5ORkxMTFYu3YtCILAkSNHgnrtgAQ+MDCAixcvYtWqVUhMTJzgcVatWoWkpKSwnvSQnZ2Nqqoq3L59Gzdu3ACAkHjv//znP2hoaMCzzz47YRJFOGA2m9HU1AQOh4MVK1ZQdWKz2Xj11Vfxz3/+Ez09PUG7/pwFbrfboVAowOVysXLlyik9T1VVFerr68PWi/s8TWVlJVpaWqDX6+dd3FqtFgcPHsS2bduwbt26UN8Sv1Gr1aivr0dpaSkWLFgwQR+5ubnIycnBF198EbTrz1ngRqMR3377LUpLS5GQkDDlw0lPT0dycjLq6+uZtHle4fF42LVrF6RSKU6fPg2n0zmvAv/ss8+wZcsWPPPMM+BwOKG+HX5ht9vR0NAAoVA4wXuPLzt27EBLSwv6+/uDYsOcBO71etHZ2Ynh4WGUl5dP+3AEAgGKiopQU1MDl8vFtO3zhlAoxOuvv47W1la0tbXNm7iPHTsGAHj77bfB5/NDfBf8x2Kx4Ny5cygvL0d8fPyUX3mxWAy5XI7a2tqg2DAngXs8Hpw4cQKVlZXgcrkgCGLKwuFwkJOTg7i4OKoHIFxJTU3Fr371K+pzGuyG5a1bt3D48GHs2bMH8fHxIa793Ghvb4dWq0VFRcW0LzGfz8fq1atRU1MDh8PBuA1zErher0d9fT02btw4qxeSSCRIT09HY2Mj3G430/bPK0888QRKS0vx0UcfgSTJoInbbrfjyJEj+PWvfz1hNnq48eWXX+Kxxx6b1gESBIGYmBhkZWUFLZSdk8APHDiA9evXQyKRzPqwhEIh8vLyoFKpgtpani/eeusttLS0oKWlJShhie/rmJKSgqeeegoxMTGhrvKc0Gg0uHTpEh566KFZ65yUlAS5XE51xzKJ3wLX6XQ4fvw4tm/fTtsjZWZmgsvl4urVqwj3CUQSiQR/+MMfcOzYMeh0Osa9d19fHzo6OvD444+HTU7MVPzpT3/Cww8/DLFYPGud+Xw+li1bBq1Wi9u3bzNqh98C/+abbyAWi7F8+XLaD00ikUAikUCpVMJoNDJagVCwZcsWSKVSnDlzhlFxW61WfPfddygvL8eqVavC1nvfvXsX1dXV2LFjB+26Z2RkICEhAQqFgtG1UvwW+IkTJ7B9+3a/PrtcLhfZ2dkwmUxQq9WMGR8qCILASy+9hPb2dvT09DDasNTr9Vi/fj0WLlwY6mrOmXPnziErKwvZ2dm0NZKYmAiZTIb+/n5Gh+/9ErhOp0NbWxsefPDBGRsOU5WMjAyYTKawHfQZD0EQWL58OYqLi1FbW8uIuM1mM9ra2rB06dKwX5H21KlT2LZtm1/153A4yMrKgs1mg0qlYswWvwSuUCiQlZUFkUjkl/EEQUAikYDH46G/vx92u52xCoQKPp+Phx9+GBqNBl1dXQELfGBgAFqtFmVlZWHbLQgAo6Oj6OzsnJMTTE9Ph91uD53AfSOXACjh0i2+7iCmP0GhgiAIZGVlQS6Xo6mpKSBx22w2XLlyBUlJSWGZQz+e5uZmLFu2bNqBnZmcoFgshkgkQn9/P6xWKyP20BY4SZJoampCWVnZ//9jP4wH7iUvqVQqjI2NMWJ8qElMTER5eTn6+vrQ09Pjt8fylZGREfT29mLTpk1gscJ7Hvh3332HkpISEAThtxMkCAKZmZkYGhpibFll2nfzypUrSExMnLDIpj+GA8CSJUtgMBig0WiCvqrofLFs2TIkJyfj+vXrAPwf4fR6vejq6oLBYMDq1atDXJvAsNvtaG9vR3FxMXXMn3sBAHK5HBqNBlqtlhGbaAtcoVBAKpVS6wz63lC6hgMAl8tFTk4Obty4ERFxOHBvCD8jIwNKpRIGg8FvgdvtdjQ3N2Pr1q2Ii4sLdXUCorW1FYsWLZow08ifLzwASKVSuFwuqNVqRka+aQu8o6MDqampExbSpCPyyZNKZTIZVCpVxKyPTRAEioqKqMaRv5/k0dFR9PT0YMOGDaGuSsBcvnwZSUlJ4HK51DE692C8E+RwOJDL5ejq6oLNZgvYJloCt1gs0Ov1yM3NnZCyOZvAp5oxnZaWhv7+/qAk1oSKnJwcxMfHo7e31+8clWvXrkEqlUbEbmw3btyAVCqlBD5ewP7oJC0tDWq1mpGvPC2Bq9VqxMXFTZmySSf2nmz80NBQWKfPTiYhIQHZ2dlQq9UwmUx+CbylpSUsJzJMxmQywWQyITMz0y8nOFWjOjU1dX4FPjAwAD6fP+0Uf38ELhQKERcXFxEDPuPJy8uDVqul9p+hW5qamrB27dpQmx8wQ0NDiI2NZcwJDg8PMxLG0hZ4QkLClI0gf41nsViQSqW4fft22CdejWf58uUYHh72S+Dt7e0QiUQTdiALV1QqFeLi4qYdpPJHI3w+HwKBAIODgwFrhJbAVSoVBALBtK18uob7kMlkuHnzZkQJXCgUQi6X4+bNm3C5XLTCk3PnzqGysjLs+76Be/sS8Xi8KQXuj7h9v5dKpVAqlQF3J896Z10uF4aHhyESifwOUaaDJEncunVr7lbfpxQXF+PWrVu0Ykev14va2lps2rRpHiwLPoODg+Dz+X578OlISUnB7du3gy9wnU5HbRw0E/4Yv3LlyojcJ7K4uJjq3potPLFarWhrawv7oXng3m57IyMjEAgEjDnBmJgYage/QJhV4FarFQRBTOjbnAq6hgP3Vo7S6/URFaIA90bh7HY7hoeHZxX44OAgsrOzZ72v4YDBYKDmV86EPwLPzc2FxWIJfgzuW1+QyZ3SBALBvC2fO58QxL0ErMHBwVkFrlarw2r5tZnwDcgw7QQNBkPAAp9VtT4PTmdNjvFGz2QYn8+H1WqF2+0O21kr05GWlgaNRjPrAxwcHIwYgVutVni9XkbXbUlISGBk9hdtDz6b8XTfTODe14DH40Gv19M0M3wYL/D/FQ/uj8Dp6oTP58Nutwc8IMiYwP1lwYIFjGWM3U/4RmqBmRtWKpUqIvq/AVCxsj8hymywWPcmIwc6d4CWwOk0Mv2Fy+UykkxzvyGVSimBTxWm+Y5FQ5TZWbBgQcB54bMK3NdNQ+eto/Ob8eeNtPgbuJdHQScNwWg0YtGiRfNgUfDxzb5h2glyOJyAk/JmFbgvKZ/pLj2SJCNS4IsWLfpeF+hUn2U2mx1RGZUA806QJMmAe+9oCRyYuVdkLjBh/P2I78Wd7UFyudyIyaj01ZXpWVpMOEF2U1MTiouLERcXh8OHD8NoNILNZiM/Px8VFRVwuVzo6upCdXU1Fi5ciM2bN0Mul8NkMqG6uhoejwd8Ph/r1q1DTk4OlEol6uvr4XA4wOFwsGHDBiQmJkKpVKKpqQlWqxVcLhdWqxVsNhvXrl3DxYsXAQAZGRlYu3YtRCIRzp49i56eHng8HojFYjz99NMwm81QKBTUMH9xcTFKSkrA5XLx97//HSaTCWw2GwUFBSgrK8PIyAjq6uqoOG7Tpk1YunQp7ty5g7Nnz8JkMiEuLg6PPPIIpFIpBgYGcOrUKQCASCTC+vXrkZ6ejtbWVrS2tsLhcIDL5eKVV14BSZLUwvQAkJmZifLycmokb//+/SAIAjKZDFVVVbBYLGhsbERXVxeAeyPETqcTDocD1dXVVIN7zZo1KC4uxsjICGpqamCxWMBms1FRUYH8/HyoVCo0NDRQPVC7du3CwoULodFocPz4cQCAWCxGRUUF0tLScOXKFbS1tcHpdILD4eAnP/kJCILAtWvXoFAoKNvXr18PPp+P8+fPU/dXLpfj4Ycfhtvtxrlz56jZ7oWFhaioqIDBYMC3336L2tpa3Lp1C0VFRZDJZLBarThy5AjYbDa1uGZBQQG6u7uhUChgNBrh9Xrxwx/+EDweD8PDw/jXv/4Ft9tNLbWckJAAm82GY8eOQaFQYOHChdi+fTu4XC4uXbqE1tZW5Ofno7S0dMaZUGxfAwG4NyKl1+vB4XCouIogCDidTphMJsTExFBex+PxwGAwwO12w+VyUamNLpcLBoMBNpsNsbGx1LQjp9MJo9EIi8UCHo8Ht9sNNpsNo9FItZQTExNBkiSA/59kQZIkJRqPxwOLxUL9frLtBoMBHA6HarySJAmTyUT93mej2+2mfs/j8ag6uVwu6rcEQVDH7XY79Ho97HY7ZYvX64XD4aB+n5ycDJIkqXrpdDoQBIEFCxZQtpvNZip8YbFYcDqd8Hg8E2z05bGQJAmDwQCTyTQhFnW5XBPumc9rut1u6lhsbCxlu81mg16vpxyOz3a73U79XiwWU+cZf399PWherxdms5k67ru/vjpZrVY4HA64XC4qnPWNbpIkSdnudDopjXm93gm2+541i8WiNECSJKxWK3Q6HbVuo+/6Op1uwvOfjln3yayursb58+exZcsWZGRkID4+HrGxsYiLiwOHwwGbzaZWJ/J9qnzG+8TvcrngcDjgcDhgt9ths9nw/PPP49///jdkMtmMBoYber0e69atw7Vr1wBMjL/Ht2WeeeYZ/PKXv4yIXPBTp06htrYWW7ZsQWZm5owaGd+mm6wRp9MJu91OaeS1117D559/jmXLls3ZtlljcC6XC6/XS71VTOB785OSkhg75/2Cz4PPBp/Pj5iBLjptDh/+tOUcDkfAE7FnfRICgQAAGJ0kbDQawefzw25LDjqMDwV8TPVQMzIyImbLc1/3IJPrv5MkyYgTnNWDCwQCKt6cDbrdiXq9HomJiX51GYULg4ODtMIuuVweMTnxCQkJYLFYjHZ7Go1GCASCgHtRaAkcmN2D+8RNR+Q6nS4iwxMA6Ovro4bgp3qBfcd8s38iAZ9GZhM4XX0A95zgokWLAnaCs4YoQqEQHo+H0bdTr9dPWCErkujv76cEPtOD9K394fF4wn7KGl2BA/RjcIPBwMhXftY7m5CQAICe8XQZHR1FSkpKRIYoPg8++Ys2uUgkkglddeFMMDSi1+uRnJwcfIFzuVzw+XxYLJYZGxH+hCgajQZZWVn+WxsG9Pf30944qqCgAB0dHUG2KPjw+XwQBAG73c7YiPfo6CgkEknwBQ7cmwVvMpmmnUzr69OcXKZjYGAAS5cujTgPPjo6CpfLhaSkpCnvx+RSWVmJCxcuhNrsgOFwOBAKhbBYLDOmH0yu/0wvg0ajwZIlSwIO32j968WLF8NsNk/7CZruMzwVRqMRLpcLKSkpc7f6PqWzsxNLlixBXFzcrCGK1+vFxo0bUVdXF2qzGUEqlcJqtc7oBOlqBLiXLy+Xy+dH4Onp6TCbzVMaP9MDnAqNRgOxWBzWuxhMR2trK3JychAbG0tL4L7VBQYGBkJtesD4clCmy/H3RyMGgwEej2d+YnCAXohCtwJDQ0OQyWQROcjT3t6O3NzcaZdOmAyXy0VhYSEuXboUZMuCj0wmg81mm1Lgc3WCTCwnTUvgYrGYSiCabNRsXmoyQ0NDWLx4MW0RhAvd3d1gsVhITU0FQRC0YnCPx4OysjI0NTWF2vyA8YUo/nrwqTQyPDyMtLQ0RjRCO8DJy8tDX1/fhEYEnc/w+E8MSZLo6enB0qVLI07gN27cgFgshlAopHVffGXVqlW4cuVK2C+EtHDhQsTHx2N0dPR7eUv+OkG1Wo309PT58+DAvdzryQIHvt8ynqk3RavVgiRJyGSyiJrs4HK5cP36daSlpUEkEvkl8NTUVCxbtgznz58PdTUCxrdl+/hR7+l62MaX8U7Q7XZjYGCAykoMFNoCLywsxMDAAPUJomP45K6g/v5+SCQSCIXCgA2/n1CpVBgaGkJ2djZ4PB7t8MTj8SA2NhalpaWoq6sL+10vCgoKJgjc9+xne8nHO8G7d+/C4/F8bzeRuUJb4FKpFPHx8ejv76eO0X2IPvr7+yGVSqlJAJFCZ2cn4uPjkZ6e7pe4fROv8/LyqK1MwpmCggIMDQ3BbDZTx/x1giqVCmKxmLGdnmkLnCAIrFmzBq2trdQxup9hXy7L4OAgpFIpRCIRI8bfDxiNRty8eRMSiQTJycl+hSe+kpSUhCVLlqC5uTnU1QkIsViMxMRE9Pb2Usf8dYIqlQoSiYSxFQf86kVfv349NY/PHy8F3Os98Xg8SE9Pj6j427dDcU5ODjgcjt8e3OPxQCQSYdmyZWhvb8fdu3dDXaU5QxAESktLJ6Qf+OMEbTYbBgcHkZqaythX3i+Bl5WVYXR0FL29vX4/xP7+fgiFwoiaouZ2u9HW1gadTofc3Nw5idvXyJLL5fB6vbh69WqoqxUQ69atw+XLl2m30caHKUNDQ/B6vVi8eDFjS4r4JXAul4tNmzbhzJkzfn2CSZKEUqmEQCCIKIFrNBp0dHSgoqLC796TySUzMxMymQwNDQ2MLDoZKlatWgWr1UotXu+PwFUqFXg8Hu1kNTr4PdC/fft21NbWgiRJ2g9Po9HAbDYjNzc3ItbDBu6FaN3d3ejp6UFpaemcvff4MK6goABGo5HaNTkcIQgCjz/+OE6dOuXXC+52u9Hb2ws+n8+oE/Rb4BUVFRgbG8OtW7dAkiStMjg4CKfTiZycHMYMDzUGgwE1NTVYv349kpKSAvLevpKTk0NtLehbsiEc2bp1K86dOweHw0H7BR8eHobBYEBeXh6jTnBOqVo//vGPcfLkSVqGOxwO9PX1IT4+HnK5nDHDQ4nX68XNmzfR1dWFtWvX0n7RZyscDgcPPfQQOjs7w3qTruLiYpAkic7OTtoCHxoagsViQV5eHqO2zEngO3fuxNWrVzEyMjKr4VqtFn19fSgpKYmYDEKn04n9+/ejsrISycnJAYcn40t+fj7i4+NRV1cX1l78xRdfxIkTJ2jV2Wazobe3FwkJCYxPhJmTwLOzs5GZmYnm5uYZPZLb7cbQ0BCGh4cjYrMlHydPnoRer8eGDRsYFbfH4wGXy8WOHTvQ3NyMGzduhK0X37lzJzo7O6HRaGb9co2NjUGpVGL16tWM5J+MZ04Cj4mJoeIst9s97cOy2+24fv06MjMzI2IvdgC4c+cOfvvb3+K5556jJmQzXZYsWYLc3Fx89dVXjC64NJ/IZDIUFhbiwoULM9aVJEloNBoMDg6ivLyccTvmJHCCIPDAAw+Ay+Wira1tWuNNJhPa29vx2GOPRcxSyQcPHkRRURFWrlzJWOw9uXi9Xjz11FPo7OzE2bNnQ13lOfPkk0/izJkzcLlcM7bR2trasHz58qCstDDn+UBJSUlYu3Yt6uvrp31Qra2t4HK5WLNmDZM2h4z6+nqcOXMGb731FlgsVlC8t68IBAI8/fTTeOeddxhdMWo+KSoqQnJyMpqamqbViMViwaVLl1BVVRWU5TPmfEYej4d169ZhbGxsyk59kiRx/vx5bNu2LSKG5q1WKz744APs3LkTsbGxQRW3r6xduxYFBQV47733wjIWFwqF2LhxI+UEp6pjS0sLEhISgtZGC+iVkclkyM/Px+XLl6mlgH3lxo0bUCqV2LZtG1O2hgyHw4HPPvsMWVlZKC8vD1poMlV5/fXXcfz48bCcnBwbG4vy8nK4XC50dHR8T9xOpxNnzpzBrl27gmZDQAJPSkpCRUUFBgcH0dvbC7fbDbfbDafTiUOHDuGNN94I+65B35eoubkZjzzyCGJjY+dV4Hw+H6+88goOHDhAa++f+43U1FSUlJTg0qVLsNlsE+rmSy579NFHg3b9gIOeFStWICMjA+3t7bDZbPB4PLh58yb6+vrwgx/8gAkbQ4pSqcTx48dRXFwMiUQyr+L2lfLycqSnp+PTTz/F2NhYqG+JX4hEIlRUVECn06Grq4uqk8PhwOeff45f/OIXjHcNjidggScnJ6OsrAxqtRoqlQoOhwOHDx/Gm2++Gfa7iN29exfHjh2DSCRCaWnpnNNhAy0xMTF48MEH0dPTg6+//jrsNq/Kzc1FTk4OWltbYTab4fF4cO3aNZhMJlRVVQX12ow0W9esWYO0tDR0dHTg4sWL8Hq92LlzJxOnDhkmkwnHjx+HUqlEWVkZhEJhSLy3r3GWmJiI8vJyXLhwAS0tLaG+PX6xcOFCrFmzBmNjY+jr64Pdbsc//vEP7N69O+iTXxjp3vBtTvXxxx/jypUr+PDDD8N6WprL5cI333yDEydOoKqqCikpKSDJ0A64sFgsrFixAnq9HkePHkVycnJAW3vMNw888AAaGxvR3t6O3t5eCIVCbN26NejXZaz/rrS0FCUlJXA4HFi3bh1Tp513vF4vOjs78dlnn6GyshI5OTmUJ/Vl/fl+N91/g/mbzMxM9Pb24q9//St2796N1NTUYN0KRuHz+diyZQs++OADXLhwAQcOHJiXyeezbkLlD74RKy6XG7YLazocDmRlZeHOnTvgcDhgsVjf22Pdn/+f7thUf08+x/iBD9//+3Z/i4mJwd/+9jdUVFQE83YwisfjwaeffoqLFy9i796987I+JaMCjxLlfiO8txaIEmUWIkbgXq8XarV6wrIWTODrqosSngRd4B6PByMjI7h169aEBWGYxuVy4eTJkzhy5Aij5/V4PFCpVLh+/fq0q+tGuX8JqsD1ej2+/vprHDp0CGq1OqgJQ263G+3t7YxPeWKz2SAIAvX19fjkk0/Q2NjI6PmjBJegpPnZbDacPHkSR48ehU6nw7PPPotVq1ZRu3ExRWNjIw4dOgSTyYQHH3wQ3d3deP755xm9BnBvh4vNmzdjz549OHr0KCorK/Hkk0+irKyM8WtFYRbGe1GsVitefPFFNDc3Q6PRIC4uDllZWdROXP7y7bffTrlYflNTE95991288cYbSE1Nxe9//3toNBo0NDSAx+NNea5A94VXqVRQq9WIj49Hbm4u3nrrLezYsSOouRRRAoNxDx4fH499+/Zh//79eO+995CWloa9e/fOecmI6XLJv/jiCxQVFWHjxo1YsGABHn/8cVRXV08rbgABx+d79+7Fp59+isLCQjz11FPYsGFDxK1zHnF4g4jRaPS++eab3g0bNni7uroYO29fX5/30Ucf9Z47d4469tprr3l/97vfMXaNyezbt8/76KOPej/88EOvTqcL2nWiMEtQp9oIBALs3bsXvb29uHbtGvh8PiNDyyaTicot9v535awvvvgCBw8eZMDqiXj/u16gSCTC/v37sXjx4rAdpYHf9gYAAACbSURBVP1fZF7mkmVmZiIzM5Ox8yUlJSEtLQ1NTU1gs9nYt28f2Gx2UKY9uVwu5ObmorCwMCKm3v2vEbZD9TU1NaiurobZbMbbb7+Njz/+GAcOHAi1WVHuM8JW4FGi0CFihuqjRJmKqMCjRDRRgUeJaKICjxLRRAUeJaKJCjxKRBMVeJSIJirwKBFNVOBRIpqowKNENFGBR4lo/g8Ye9OyIK4z5AAAAABJRU5ErkJggg==)
Physics-General
Physics-
A medium shows relation between i and r as shown. If speed of light in the medium is n c then value of n is
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)
A medium shows relation between i and r as shown. If speed of light in the medium is n c then value of n is
![](data:image/png;base64,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)
Physics-General
Physics-
The graph between sine of angle of refraction (sin r) in medium 2 and sine of angle of incidence (sin i) in medium 1 indicates that (tan 36° >
)
![](data:image/png;base64,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)
The graph between sine of angle of refraction (sin r) in medium 2 and sine of angle of incidence (sin i) in medium 1 indicates that (tan 36° >
)
![](data:image/png;base64,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)
Physics-General
Physics-
The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used
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kEGzduhEwmw7Zt2yiEZECoR3xMHMfhs88+Q1paGpydnZGTk4OXXnqJQvgT48ePx9ChQ4UuQ7QoiI+ho6MDhYWFSElJgZubG5KSkjBt2jQK4f9otVrodDpIpdIee0zVajWsrKzo0hkPoFfiF1IoFCgsLERycjJcXV2RkJBAe0d/QqFQ4JtvvkFbWxtaW1vR2NgIjuNw4cIFcBwndHmiQj3iL8DzPHbu3In169d3H6yfO3fuoD5O2Bs7Oztcu3YN58+fh7OzM+rr6zFixAhotVq66vdPUBAHSKFQYOvWrdiwYQPc3NyQkJCA2bNnUwh7YWlpCV9fX6xevRp1dXVQKBR45plnEBkZCXt7e6HLExUamg4Ax3HYsmULNmzY0H2wfs6cORTCPgwfPhyBgYH47rvvUF1djdGjR+OZZ54R5fzw6tWr+OyzzwRpW3yvhkgpFAps3rwZOTk5cHR0RF5eHl5++WWaE/4MGxsbTJ06FRMnTsS4ceMwY8YMDBs2TOiyeuXm5gY7OzsEBgaioKDAqG1TEPtJLpejuLgY9vb22LFjB37/+9/TIuZ+kEgkGD16NBYvXowFCxZg0qRJor2sooODA4KDg/HGG2/gr3/9K/z8/FBSUmKUtiWMMWaUlvqhqKgIixcvhlqtFrqUhzy4VpKu0TlwjDEwxkQ5JP0pxhi0Wi0kEglsbW3x/vvvIyYmxqDzWlEFkRChaTQaHD58GJGRkRg7dizee+89zJw5EzY2NgZtl4JIyP+o1WqcPXsWWVlZCAsLw9y5c412nR2a5BDyPx0dHbh37x7y8/NhZ2dn1LapRyREBMQ/cyYmpb29HVqtVugyTI7og8jzPEpKSlBTU2PUdtvb23HixAm0t7f/7O92dnbi8uXLqKys7NfvmzOpVIrS0lK64cwAiTaISqUSRUVFiIiIQEdHB0aMGGHU9mUyGRhjiImJQVFRUa93u9XpdLh69SqSk5ORn58Pe3v7QX8RXVtbW/zud7/Dtm3b8M477+Ds2bNCl2QamMioVCp25MgRNmvWLPbUU0+xnJwcplAoBrydixcvstDQUObu7s5mz57NwsPD2cmTJwdcS2FhIXv22WdZYGAgKysrY2q1mjHGWFNTE0tISGBjxoxh8+bNY2fOnGGdnZ0DrtPQSktLma+vL3N3d2dRUVFGa7epqYn5+fkxDw8PtmLFClZVVWW0tgeisbGRFRQUMLlcLmgdogqiWq1mmZmZTCaTMQAMAJNIJMzCwqLPr2vXrvXYTk1NDQsJCWFpaWmMMcY++OADNnTo0IcCnZeX97PblkgkPWqJjo5mjY2NzMnJqftn/anR0F8ajeah17O8vJy98MILrLy8nDHG2Pz581llZWWvr31gYKDea3rw9XnuuedYSUkJUyqV+nir6JVcLmczZsxgf/rTnxjP80yn0xm9BlEFsUtlZSWbNWsWc3FxYbm5uYzn+X4/V6fTsb1797JZs2ax77//njHG2OHDh9mUKVMG/Cbo6Ohg+/btY76+vszPz48VFBQwjuMYY4xpNBq2YcOG7h73m2++EVWPqNFo2KpVq1hSUhJra2szattarZbV1tay8PBwNmrUKLZy5Up24cIFg7TV3t7Orl+/zmprax/rq6Kigo0bN45JJBIWGRnJ6uvre/1wMxRRHkf08fHBoUOHcPz4cWRmZsLDwwPTpk2Dg4PDzz63o6MDV65cwfDhw+Hu7g7g/n0Xnn/++QEtr+J5HufOncPp06exZMkSvPLKK3jiiSe6f25lZYWoqChEREQgNzcXu3fvhp2dHby8vESxBvXHH39EbW0t/vCHP/TrddMXrVaL+vp6fPzxx3Bzc8O+ffvw4osvGqy9iooKbN68GR0dHY+1HZ7ncevWLVhaWqK4uBj37t3Dhg0bMHLkSD1V2jfh3zF9CAgIQEBAAL766is0NDT06w2l1WqhVCphbW0Na2trnD9/Hvv370dYWFi/g8gYg0KhgLW1Nd5///0+/xhubm5Yt24drl69irt370KpVIrmXDsbGxvodDpotVo0NjZCKpXC1dXVoG12dnaioaEBISEhRrmg8Jw5czBnzpzH2gbHcTh69Ci2bt0KR0dHhISEICgoCE5OTnqq8ueZ3QF9tVqNvXv3dp8h0XXp+507d2LatGmDZrF2U1MT0tPTUVdXh9/+9rewtrbGq6++Ci8vL6FLExWlUomqqiqcOnUKnp6emD59eo+Rj7GYXRABoKGhAWVlZWhubsbEiRNRW1uLoKAg0Z4HZyhXrlxBZWUlOI7D2LFjMXPmTJM4+8GYVCoVbt68CQcHB7i4uAj2+phlEAkxNfTxSIgIUBCJ2UpKSkJGRkb3ssN//OMfWLp0qcBV9Y6CSMyWra0tWlpawPM8dDodNm3ahLlz5wpdVq8oiMRsubq6QqVSQalUoqysDK2trZg/f77QZfWKgkjM1ogRI6BUKtHU1IRNmzYhOztb6JIeiYJIzNZTTz0FjUaD7du3Q6VSITQ0VOiSHknUK2sIeRzDhg3DvXv3cPnyZWzatEkUSw8fhY4jErOlUqlQXl4OiUQCPz8/2NraCl3SI1EQCREBmiMSIgIUREJEgIJIiAhQEAkRgf8DTLVqZ2QhHDIAAAAASUVORK5CYII=)
The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used
![](data:image/png;base64,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)
Physics-General
Physics-
The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAACLCAYAAACQniBTAAAVuUlEQVR4nO2de1QU5/2HP+wuC8hyS7goVG4CYmC5iNVDEqlWY7yemAR7bElaKtpjCmijQBoWuWhsjyWtiT1eggiEVNtaNbYpaGgP6DExtRKJgIkIiIosLHubXViW5bLv7w9lG35RuezCzML7nLMHWHZmPsN5eN+Z77zzjg0hhIBCmWR4bAegTE+oeBRWoOJRWIGKR2EFKh6FFah4FFag4lFYgYpHYQUqHoUVqHgUVjBbPL1eb4kclGmGWeL19fXhz3/+M3Q6naXyUKYJZon32WefIScnB5cvX7ZUHso0Ydzi9fb24vDhw5BKpSgoKIBGo7FkLsoUZ9ziVVRUoLq6GkajEZ9//jkuXbpkyVyUKc64xNPr9fj444+RmpoKNzc3vPHGGygpKYFarbZ0PsoUxWY8A0HLysrAMAzWr1+PwMBAXLt2DZ9//jns7Ozw0ksvjTlEaGgorl+/Djs7uzEvS7FOBEPfGI1GGAwGCIVC8Pl8AEB3dzfs7e0hEAiGLRQWFgYvLy84ODgAAJycnLBmzRq0traCYRi4urqOOsCLL76IxsZGaLVaeHh4WGKfKFaAqattaGhAYmKi6VhNr9cjOjr6kWes/v7+JumGcHR0RGho6JikAwCRSAQej4eurq7x5KdYKSbxXFxc0N/fD41GA6PRiIqKCvD5fMTFxU1oAEdHR9jY2ECr1U7odijcwiSeq6srRCIR2tvboVarUVhYiLS0tAkP4OjoCB6PR8sx0wyTeDNmzICvry90Oh0qKirAMAzi4+MnPABt8aYnw84aAgMD8a9//QsNDQ3Yt2/fmI/XxgNt8aYnw+p4np6eqKurwwsvvIDFixdPSgCRSERbvGnIsBZvyZIlOHv2LNzd3SetpjbU4lHxphfDxBOJRAgKCprUAO7u7uDxeLh79+6kbpfCLqwPBA0ICICtrS2+/vprtqNQJhFOiCcUCnHz5k0YjUa241AmCdbFc3d3h7u7O+RyOTo7O9mOQ5kkWBcPAEJCQgAAt27dYjkJZbLghHhz584FQMWbTnBCvJCQEBBCqHjTCM6IB9AWbzrBKfEaGhpAJyidHnBCPDc3N0REREClUuH69etsx5lwtFotCgsLUVtby3YU1uCEeDY2NlixYgV6e3tx5coVtuNMKGq1Gu+//z4uXbr0ncG00wlOiAdgmHhTsbslhEChUODYsWNobm5GWloagoOD2Y7FGpwRLzY2Fvb29qitrZ2Sd6splUp89NFHuHHjBrZv3w6xWMx2JFbhjHiOjo549tlnwTDMlDvOYxgGRUVFqKurQ2pqKqKjo9mOxDqcEc/GxgZxcXFTTjyNRoP9+/fjm2++wbZt2zB//ny2I3ECzogHAD/4wQ+g1Wpx/fp19Pf3sx3HbBiGwTvvvIM7d+4gLS0NUVFRbEfiDJwSz9/fH76+vqirq0N1dTXbccyCYRjk5eVBrVYjJycHYWFhbEfiFJwSz9HREYsXL4ZCoUBLSwvbccbNkHQ9PT3YtWsXAgMD2Y7EOTgn3urVq9Ha2or//Oc/6OvrYzvSmNFoNNi7dy+6urogkUjg6+vLdiROwinxBAIBxGIxoqOjUV9fb3WjktVqNfbv3w+5XI63334bvr6+sLGxYTsWJ+GUeMCDO91++MMf4ubNm6itrbWKUcmEEMjlchw9ehT37t1Deno65syZw3YsTsM58dzc3PD888/DYDDgypUrUCqVbEcaEYVCgdLSUjQ0NGD79u30RGIUcE48GxsbBAUFYeHChfjvf/+L27dvsx3piajVahQVFeHrr79GamoqIiMj2Y5kFXBOPADw9fVFbGwsbt++jbq6OhgMBrYjPZKh4nBDQwO2bdtG63RjgJPiiUQixMTEwN3dHRcuXIBCoWA70ndgGAZ79uzBvXv3kJaWRlu6McJJ8QBALBYjIiIC58+fR319PQYHB9mOZGKoKKzRaJCdnY1nnnmG7UhWB2fF8/HxwYoVK2Bvb49Tp06hu7ub7UgAHrR0ubm5MBgMyM7OpsXhccJZ8fh8PlasWIHQ0FB8+OGHaGpqYjsSNBoN9uzZA51OB4lEgtmzZ7MdyWrhrHgA4Ofnh/Xr18PV1RWHDx9mtaanUqnw+9//HiqVCpmZmVQ6M+G0eACwdu1aBAUF4fjx46yUVggh6OzsREFBAdra2pCenk67VwsgGPkj7OLv748NGzagvr4ee/fuxbFjx8Djje7/pbOzEzU1NaafPT09ERYWBqFQOKrlh65IlJaWoqmpCdu3b6cnEhaC8y0eALzyyisIDg7GyZMnUV9fP6pl+vv7cf78eezYsQOnTp3CRx99hF//+tf48ssvR31Px1Bx+ObNm0hJSUFERIQ5u0H5FlYhnp+fH37yk59Ar9dj37596OnpGXEZvV6Pjo4ObNiwAUePHsUHH3wAPp+Pq1evjupYcag43NTURIvDE4BViAcAP/7xj7FgwQJ8+umnKC8vH/HzOp0OSqUSAQEBAB48QGZwcBDOzs4jjhgZGk/X1taGnTt30pZuArAa8by9vZGbmwuGYXDw4MERyytarRbNzc2mE4HS0lL09PRgwYIFTxRPrVZj165d6Orqwq5duzBv3jyL7gflIcRMPD09iUajMXc1o8JgMJCkpCTi4uJCdu/e/cTPXrt2jTg5OZHAwEASFhZG1qxZQ6qqqkh/f/9jl1GpVCQlJYVs3bqV3L9/39LxKd/CqsQjhJDW1lYyZ84cEhkZSSorKx/5mb6+PlJSUkJWrVpFNBoN0Wg0RKfTkcHBwceul2EY8qtf/Yps3ryZSjcJWE1XO4SHhwe2b9+OGzduoLi4+JHj9fr7+9HY2IhFixbB2dkZzs7OmDFjxiPLMIQQqFQq5OfnQ6PRIDMzEz4+PpOxK9MaqxNv6NGka9aswaVLl3D+/Pnv3ApJCIGdnR1CQ0OfuC7ysDh85MgRdHR0ICMjw3QyQplgzG0yJ7urJeRBV3r69Gkya9Ys8uKLL5KampondqOPwmg0ko6ODrJv3z6yefNmUltbO0FpKY/C6lo8ALC1tcXzzz+Pn/70p6ipqUFpaemYh8irVCoUFRWhqakJKSkp034uk8nGKsUDHlz+ev311xEbG4tTp07h448/hl6vH9WyGo0G7733Hm7fvk2Hq7OE1YoHPJi0e/PmzXB2dsa7776Lzz77bMTLYUODOKVSKXbs2EFbOpawavEEAgGWLl2KzZs3Q6vVIjc394nPylCr1cjKyoJOp0NWVhYtDrOIVYsHPJh9YNOmTXj11VdRW1sLiUTyyM8NSWc0GpGXl0fPXlnG6sUDAGdnZ2RlZWHu3LkoLS3FgQMHhv2eYRjk5ORgYGAA2dnZ8Pb2ZikpZYgpIR4AzJo1C3/4wx8gFAqRlZWF06dPY3BwEEql0jSiJTMzE7NmzWI7KgVWMBB0LMTFxeG9997DW2+9hTfffBM9PT24c+cOlEol0tPT4efnx3ZEyhDmFgLZKCCPxP79+4m7uzuZMWMGWbt2Lbl27RrbkSj/jynT1X6b+Ph4zJkzB3w+HzqdDgaDgVP35VKm0DHeEAzD4MiRIwgODsamTZtw69Yt0zQTZAo+xsBamVLHeGq1Grm5uejp6YFEIoGTkxOMRiNOnTqF/fv3IycnB9/73vfYjknBFBJPpVJBIpFgYGAAEokE/v7+MBqNSE5Ohlqtxt///ncQQrB37154eXmxHXfaMyXEU6vVkEgksLGxwZ49ezBz5kwAAI/HQ1BQENLS0qDVanH69GkoFAocPnyYllVYxuqP8RiGwa5du0AIQXZ2tkm6Ifh8PsRiMQ4cOIAXXngBFRUVWLduHSemxJjOWK14hBAolUr89re/hcFggEQi+Y50Q/B4PPj5+aGwsBAbN25EfX09Vq1ahS+++IKe7bKEVYpHCIFMJsPBgwfBMAwyMjJGNZeJs7MzCgsLkZKSAoVCgYSEBHzyySejHk5FsRxWJx4hBB0dHSguLoZUKsW2bdvG9BREHo+Hd999F+np6TAYDNi5cyf+8pe/TMkH93EZqxNPLpejqKgI9+7dQ0pKyrgnuk5LS0NmZiZ4PB7y8vJw6NAhtLS00K53krCqs1qGYXDgwAEoFAqkpKQgPDx83OsSCoVITEyEi4sLjhw5gkOHDqGhoQFJSUmIjY0d9cQ+lPFhQ8ws53t5eaGxsRHOzs6WyvRI1Go1srOz0dfXhx07dmDu3LkWWa9er8eXX36JoqIinDt3DrNnz0ZycjISEhIgEFjV/6VVYRXiDU2GaDQakZmZCX9/f4uuf3BwEFKpFCdOnMD7778PgUCAhIQEpKWl4emnn7botigPMXeUwUSPTlEqleQXv/gFeeONN4hMJpuw7RBCiFarJadPnyZhYWHEycmJLF26lFy+fHlCtzld4bR4KpWKbN26lWzdunXCpRtiYGCA3Lt3j7zyyiuEx+ORWbNmkXfeeYfI5fJJ2f50gZPiGY1GIpfLSVpaGtmyZQtpbW216PpHS35+PnFzcyMCgYDExMSQiooK0tvbS4xGIyt5phKcO8YjD+t0BQUFaG9vR1paGoKCgiyy7rFiNBrxzTffID8/H+Xl5eDz+YiPj0dSUhJCQ0Nhb2/PSq6pAKfEI4Sgvb0dJSUlaG1tRWpqKifmHNZoNPjkk0/wpz/9CV988QWCgoKwZcsWLF++HIGBgaOek5nyPzglnkwmw9GjRyGVSvHLX/7SrDrdRNDY2IiSkhKUl5ejsbERy5Ytw8svv4zvf//7CAkJga2tLdsRrQazxfPz80N1dTU8PDzMCsIwDPLz86FSqcy6IjHR6HQ6XLlyBSdPnkRlZSWkUini4uKwfPlyLFu2DPPmzaPF51FgtnghISGorKw0a2Tv0PSvAwMDePPNNy1WHJ5I2tvbUVdXh/Lycnz66adob29HVFQUli5divXr11MBR4B18VQqFd566y3Y2NhAIpFY3S2ICoUCDQ0N+Oc//4kzZ85AJpMhMDAQK1euxLp167Bw4ULw+Xy2Y3IOVsVTqVTIyMiAnZ0dcnNzze6u2cJoNKKrqwvNzc04e/asadq0p556CuHh4XjppZewevVqer/HtzG3HhMcHDyuOptKpTJdkZgqxVmj0UgMBgNpbGwk+fn5RCwWE4FAQOzs7IiHhwdJTEwk//73v0lvby/bUVln0ls88nDk8G9+8xv09PRM+blMLl68iOPHj+PMmTPQ6XTo7+9HUFAQ4uLi8NprryEqKgpCoRACgWBaDUqYVPHIwzrdBx98ALlcjp07d2LOnDnmbN5qYBgGZ86cwT/+8Q989dVX0Gg06OrqQmBgIJ599lk899xzWLhwIdzc3CASiSASiab0ycmkiUcIgVQqRUlJCaRSKVJTU0ecHHsq0tvbi/r6elRVVeHKlStobW2FUqmEQqGAXq9HTEwM5s+fjwULFiAgIMAk4dDL0dFxSrSMkyKe0WjEsWPHcPfuXSgUCqSmpk5ona6wsBCOjo6IjY21+BAqSzI4OIiWlhbcuHHD9Gpra8P9+/chk8kgFArh7e39nZeHhwdcXV3h4uKCGTNmwNbWFkKhEEKh0PT90FeBQMDJKyuTIp5CoUBISAi8vb2xevVq7Ny5c8w3VVdXV6OsrAyrV69GdHQ0vvrqK5SVlZl+7+TkhKSkJFy+fBkffvghZs+eDQcHB+zevXvc+zbZdHd3o7m5Gc3NzWhqakJbWxvkcjk6OztNX1UqFRwdHeHh4QF3d3eIRCLY2dkNe9nb20MoFMLe3h4BAQFYtWoV5x7sPOFttkqlQk5ODl599VUsXboUly9fRkFBARITE0f9x2AYBrm5ubhz5w48PDwQERGBq1evoqKiAhs3boSDg4OpCzp37hw2btwIX19f5OXlTfDeWRaRSITIyEhERkZicHAQOp0ODMNArVYPe0mlUkilUnR2dqKrqwsMw6C3txd6vR56vX7Y91FRUQgPD59e4g3V6QQCAbKysuDj4wOxWIzi4mIcP34cW7ZsGdUI39LSUojFYgwMDAx7Pzg4GK+//jpcXV1N77388svYsWMH/P39ER8fb/F9miz4fL7pqUS+vr6m9wkh6OnpQXd3N3p6etDX14eBgYHHvkQiETevBJlbj3lcHU+pVJKf//znJDk5mXR2dpreHxwcJDU1NSQxMZGcO3duxAejVFZWkoSEBNLU1ERWrlxJDh48SHp7e8mhQ4eIq6srCQ0NJWFhYeTEiROkt7eXGAwGUl9fT27dukV0Op25u0eZICakxVOr1cjIyICDgwPy8vKGtWo8Hg8RERFYvnw5KisrER4e/tjjQ5VKhT/+8Y+Ij48f9l9vZ2eHpKQkJCQkAADOnz+P7OxszJ49G8899xxnBxhQ/odFT3cIIZDL5cjLy4OtrS2ysrIe2ZXyeDwsWbIEDQ0NkEqlj13f3/72N/j4+GD+/PnQ6/UYGBgwHb8IhUJTV/SjH/0IXl5eqKmpoXPgWQkWa/HIw+Lw4cOH0d/fj4yMjCfOyOTj44NFixahuroaYrEYDg4O3/mMVqtFVVUVqqqqAAB3797FzZs30dTUhN27d8PZ2RlCoRAMw8BoNCIgIGDEp29TuIFFxCOEoK2tDcXFxVCr1di2bduoniMRFRWFiooKGAyGR4qXnp6O9PR008+rVq3CunXrsH79ehQUFMDHxwczZ87EhQsXEBAQgEWLFlHxzKSrqwsdHR0ICgqa0L+lRcSTyWQoLy+HXC5HcnLyqM+i3N3dodPpRj1txMqVKzFv3jw89dRTiIyMxNmzZwE8qOHt3r3bake3cAmGYVBVVYWLFy8iOjoaMTExE7IdswvIAQEBWLNmDQAgOTl5TI9pkslkOHnyJH72s59N+EwElNFz//595ObmorGxEWvXrsWyZcswf/58i27DbPG8vb2h1+sRERGBkJCQMS/f2dmJp59+mg6W5Bjt7e0oKyuDvb09Fi1ahE2bNmHDhg2PPCQaD2Z3tSdOnIDBYLBEFgqHaGlpwcWLF+Hi4oKFCxciPDz8kTczHTx4EMHBwVixYgXa29vx17/+FTExMVi8ePET12+2eEuWLDF3FRSOcfv2bfzud7/D1q1b8dprr8HPzw/Ozs6PHGxQWlqKrKwsAA+uyUul0lF1y9Y/voZiUWQyGS5cuIDi4mLMnDkTtra2jz27vXv3Lm7dumV60HRbWxu6u7uHXcJ8HFQ8yjC8vLywadOmUX22tbUVtra28PX1BSEELS0tGBgYeOxc1N+GewO1KFbD1atXERcXB6PRiIaGBly4cAF+fn7w9PQccVkqHmXceHp6QiaToaysDKWlpWhqahpVawdYoJxCmb4oFAq8/fbb4PP5mDdvHp555hnMnDkTYrF4xGWpeBRWoF0thRWoeBRWoOJRWIGKR2EFKh6FFah4FFag4lFYgYpHYQUqHoUVqHgUVqDiUViBikdhBSoehRWoeBRWoOJRWIGKR2EFKh6FFf4PrLV4/98l8owAAAAASUVORK5CYII=)
The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v
![](data:image/png;base64,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)
Physics-General
Physics-
Three right angled prisms of refractive indices
and
are fixed together using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation, then
![](data:image/png;base64,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)
Three right angled prisms of refractive indices
and
are fixed together using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation, then
![](data:image/png;base64,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)
Physics-General
Physics-
The distance between a convex lens and a plane mirror is 10 cm. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of lens will be
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)
The distance between a convex lens and a plane mirror is 10 cm. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of lens will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAACgCAYAAAB6xDygAAASfElEQVR4nO2da2xT5R/Hv+f03nXrxjrYBTbYRgbjNsZ13AyLk2nQIEpM8AUBDSrwwij4xjfiJSZERYQoEUUIUfGNOhMQcUMuc4NdFGFyGQ4cjLJ713Vt167t+b9Y2v+6re1aup3zzN8necJ2znPa54FPfjz3wwmCIIAgGIQXuwAEESkkL8EsJC/BLCQvwSwkL8EsJC/BLCQvwSwkL8EsJC/BLCQvwSwkL8EsJC/BLCQvwSwkL8EsJC/BLCQvwSwkL8EszMsrCAI+/fRT3LlzR+yiEGMM8/JeuHABu3fvxkcffSR2UYgxhml529vbsW/fPphMJtTU1KC0tFTsIhFjCNPylpSUICYmBgqFAk8//TTeeustWCwWsYtFjBHMynvt2jWUlZVh9erVeO+997Bs2TKkpaXhyy+/FLtoxBghF7sAkSAIAn766SckJiYiPT0dsbGxAICNGzdiz549KCoqwqxZs0QuJQEAhw8fRlxcHOLi4qDT6RATEwOtVguNRgO1Wg2lUgmlUgm5XA6ZTAaO40b82UxG3vLycty+fRtLliyBXq9He3s7eJ6HwWDAypUr8fXXX8PpdIpdTGKUYU5ei8WC8vJy6HQ6TJ06FTzPY8eOHeA4DhqNBgUFBWhsbERVVZXYRSVGGabkFQQBly9fRkNDAxYtWgSdTgee52G328HzPHieR1JSErKzs/Hrr7+iu7tb7CITowhT8nZ1daGyshKxsbHIysryCTtx4kRwHAee56HT6TBnzhw8ePAAtbW1YheZGEWYkdfj8eD69euoqanBqlWroNVqffJu27YNcrnc93tGRgbS0tJQUVGBjo4OsYtOjBLMyGu1WvHbb79hypQpyMzM9InK8zxWrlzp93tMTAzmzJmDu3fv4tq1a2IXnRglmJG3paUFpaWlKCoqgkql8pP17NmzvmaDN2VnZyM+Ph61tbUwm81iF58YBZiQ1+PxoKSkBLm5ucjIyADHcX5p7969AOB3TaVSIS8vD3V1dWhqahK5BsRowIS8brcb3377LZ544gm/tq032Wy2Idd4nsfChQvR19eH6upqOBwOsatBRBkm5D106BBycnKQk5MzJOpyHIeEhATwPD/svUceeQTnz5+njts4RPLyWiwWHDt2DM8888ywcnIchw8++CCgvEuWLMG9e/dw5coVeDwesatDRBHJy3vq1Cno9XrMnz9/2KYBz/PIyckJeE+r1aK4uBgnT56E2+0WuzpEFJG0vG63G8eOHcNzzz0XUE6e5/HDDz8MGW0YmFasWIGrV69Sx22cIWl5r169is7OThQUFASVd//+/UHlTU1NRU5ODn788Uexq0REEUnL+/3336OwsBA6nS5ge5fjOPT19QW9z3EcnnzySRw9epTaveMIycrb3NyMqqoqrFmzJmjU5XkeU6ZMCZln1qxZiI+Px/nz58WuGhElJCtveXk5MjMzfYtugqVDhw75FjIHSiqVCoWFhSgpKRG7akSUkKy858+fx+zZs6HRaEJG1aSkpJB5eJ5HUVERfv75Z7GrRkQJScrb2NiI1tZW5ObmQqlUjijyAgiaBwDS09MxYcIEVFdXi1k9IkpIUt6amhqkpaVBr9eHFJfjOBw8eBBAaHkBYPny5SgrKxOrakQUkZy8TqcTf/31FyZPngy9Xg8guJQjTV4KCgpQUVFBe9zGAZKT12g0orOzE+np6VCpVABCy7tq1aqA08ODBZ4+fTrsdjsaGhrErCYRBSQn761bt6BSqWAwGHzXQnXEdu3aFfT+wMirUCgwc+ZMVFRUiFE9IopITt6GhgaoVCpMmDDB73qwiOrdRRyqyQD0y5ubm4uLFy+OZbWIUUBS8nZ1daGlpQVJSUnQ6XR+94LJu3PnzpB5vHj3uFksFty9e3dM60dEF0nJazQaYbVakZKSMiRiBhPTO3oQKup68+j1eiQmJuLy5ctjUi9idJDUcU9NTU2wWq1ITk4e9v5wMgKAy+UKKOtwaLVaJCUlUaeNcSQjryAI6OjogMfjQWJi4rB5Asm5dOnSIR2zgZ87GJVKBb1ej3v37kEQhBFLT0gLyTQb7HY7Ojo6oNfroVarh80TqNlw5MiRgB224ZDL5UhISIDNZqOdxQwjGXm7u7thMpmQlJQUNN9wgjY3N49YXC8xMTGQy+V48OBBNKtBjCGSkrezszOkvMPx8ccfD9s8CIZOp4NMJoPRaAz7+whpICl5TSYTJk6cGDAPxw2/W6KkpGTIvVCRV6fTQaFQkLwMI4kOmyAIMJvNsFgsI4q8gYbAwul4xcTEQKlUoqWlJayyEtJBEpHX6XSipaUlaGctGK+++mrYIwZKpRJxcXGwWCzo6ekJ+zsJ8ZGEvA6HA0ajEampqSHzDtcx27Jly7CjDaE+R6/Xo7e3lw4kYRRJyGu323H37t2AkxODGSymVquN6Hv1ej0cDgfa2toiep4QF0nI29vbC6PRiJSUlBE/M3hJpHeyIZy2r0ajgcfjgc1mi7TohIhIosPmcrlgsVgQHx8/4mcGCmo0Gv2kHemwmUqlgtvtht1uD6/AhCSQROR1uVyw2WyIiYmJ6HmNRhPRcyqVCi6Xi+RlFNEjryAIvv+2lUrliJ8bGHk3b97sN7Y70sirVCohCAJ6e3vDKDEhFSQhr9lsRlxcXNjPemV94403/D5vpKhUKpKXYURvNgiCAJPJ5HuLZSTU1NT4fg5nvFcul0Mul8PhcNAJkgwiCXm7urqG7JwYKRzH4c0334x4aaNGo4HD4aDdxAwiCXlNJlNE8nplra+vj/j7NRoNnE4nycsgkpD3YSLvw+KNvPTOCvaQhLydnZ0P1ebdt29fxLshFAoFXC4XXC5XxN9PiIMkRht6enoiHqvlOA7r1q3zfVa4eDyesFekEdJA9MgL9G9Hj0Q8L1VVVRE/P3BamWAL0eX1LiJ/mKGqrVu3RnziuTfy8rzofxVEmMjffvttUQvgdrtx+fJlNDU14datW5DL5ZDJZOB5HjKZzPezdwZt8NJHAPj333/x7rvvguM4CILgSx6PBx6PB4IgwO12w+Px+P50uVxwu92or68Hx3GwWCwRT08TgZk8efKofbZ8pMsQRwuXy4XY2FhotVokJib6Jg684g4WeKDIXnkNBgOSk5P95PWK601ut9sveTtp3o2YkyZNEm3Eg4gM+datW0UtgMPhwI0bN5CSkoI1a9ZApVJBqVRCoVBAoVBAqVT6ZB4YlQdKPGfOHCxZssQn7+Do6na70dfX55ecTiccDgfkcjnUajU2bdoU8LwIInIOHz48ap8tiYaeQqF4qLf0FBQURNzhog4bu4gur7cd+zDynjlzJuLRBhoqYxfR5QX6F8g8zGjD5s2bI37W4/H4miAEW0jiX0ypVEYsrzfiRhp5e3p6oFKpfKewE+wgurwcxyExMfGhzgzLzs6O6DlBEGC326HRaEheBhFdXu971B5G3vfffz+i//Z7e3shCAK0Wi21eRlE9LUNHMchKSkJJpNp2Pvl5eX4888/wXEctFotli5dimXLlgH4/0jBokWLfL+Hg91uh0wmi3jrPCEuokdejuNgMBhgMpmGyHfgwAEcPXoUcXFx0Ov1MJvN+OSTT1BZWenLIwgCDhw4ENFoRW9vL3ieJ3kZRRLyxsTEgOM4v128586dQ0VFBZ5//nm88MILePHFF7Fp0yYolUqUlpYCgG827eDBg75p4HCir91uh1wup5k1RhFdXqB/qEyv16O7uxtA/4mR3333HVavXo2CggJfvri4OEybNg1Wq9Xv+UjPGuvt7YVCoSB5GUX0Ni/QL29cXJyv03bv3j309vZi+fLlftvh+/r64PF4kJCQ4Bdhk5OTw466wP/lpQU5bCKJyKtQKJCQkOCLvCaTCXq93tec8NLS0oL6+nrMnDnT7/nff/89otEGq9UKmUwW0bZ7QnwkIa9SqYTBYPCd1iiXy+FyuWC1Wn3R1GQy4eTJk1CpVL6zybzJZrP5/T4SPB4PzGYzlEolEhISRq1uxOghiWaDWq1GWloarly5AgCYNm0a5HI5jh8/ju7ubqjVatTU1KC2thavvfYa9Hq9n6RfffUVXn755bDGam02G2w2GzIyMiCXS+KvgQgTSURelUqFlJQUtLW1weVyYdKkSdixYwc4jsM333yDI0eOwGg04rPPPvPrwHn58MMPw27vWq1WOJ3OER+rSkgPSYQcmUyGxMREcByHrq4uaLVaZGVlYffu3UPW8waSdHCTIZTMPT09cLvdYR2rSkgLSUReAIiNjUVCQgJaW1tD5h3YvhUEAY899tiQ66GwWq1wuVwkL8NIIvIC/WO4EyZMCHlK+XBi7tq1K+C9QJ9hsVgo8jKOpORNSEgIKm8gOadMmRJWm7evrw9msxkGg4FWkzGMpJoNer0ezc3NYXe+tmzZEva0cEdHB6ZOnRpuMQkJIRl5ZTKZr+cfKvoOThUVFX5rG0K1fW02G9rb24dMdhBsIRl5ASAtLQ1arRbNzc3D3h9OTu+yyJGK6z1eymQyYcaMGaNZHWKUkUybFwBSU1OhVquDyjscBQUFIx5l8Hg8aGxshMFggMFgeKjyEuIiKXkNBoNvuMzpdEKhUPjdDyTn559/HvD+4GsulwsNDQ2YN29elEpNiIWkmg0ymQxZWVmw2WxD3koZqMkgCAIePHgw4javy+XC7du3kZ+fP1bVIkYJSckLAJmZmXA6nejs7PS7Pvj4poFpz549Qe8PlNhkMsFkMiE3N3esq0ZEGUnK29fXh9bWVr9t7cHS6dOnA0bewdG3rq4OmZmZtAxyHCA5eXU6HTIyMmA0Gn3vZwsl70jzAP1rfwsLC0WpGxFdJCcvx3FYsGABjEajb2dFKDG9hwWGyud2u3Hu3DkUFRWJWUUiSkhOXgBYuHAh7t+/P2J5X3rppZD5gP4zzfLz8zFx4kTR6kZED0nKGx8fj7y8PNTW1voOBgmWurq6RtRs+OWXX/DUU0+JXDsiWkhSXgBYtWoVrl69CrvdHlLM7du3w+12B81jtVpRXV2N4uJisatGRAnJypufn4+2tjY0NzcHHQbzeDy4fv16yDwVFRWYMWMGUlNTxa4aESUkK298fDwWL16Ms2fPhhTTezh1sFRaWor169eLXS0iikhWXgBYu3YtTp8+DafTGVTMHTt2AAg8kXH//n00NjbSKMM4Q9Lyzps3D3q9HpWVlUHbsxs2bAh6/8KFC8jLy6PNluMMScurVquxceNGHD9+PGjkvXnzZsB7fX19KCsrQ3FxMWQymdhVIqKIpOUFgPXr1+P69eu4c+dOwMi6c+fOgNPDV65cQXx8PHJzc+no/nGG5P81NRoNNmzYgBMnTgSMru3t7b7XVw1OVVVVWLhwIeLj48WuChFlJC8vAGzatAllZWVwOBzDRle1Wj3s9ebmZty8eRNLly59qLfKE9KECXmzs7OxaNEinDhxYlhJt23bBsB/etjj8aC2thbTp08f1VeIEuLBhLw8z+PZZ59FZWUlurq6hjQN1q5d6xPWm7q7u3Hz5k3k5ubSKMM4hQl5OY5Dfn4+DAYDLl26NETe8vLyIddu3LgBmUyGvLw8vzN+ifEDE/IC/YeSrFmzBtXV1TCbzX6i7t+/36/DZrVaUV9fj/T0dGRlZYlddGKUYEZepVKJuXPnQq1Wo66uzq9929ra6jdU1tTUhLa2NsyfP5+O7B/HMCMvAKSnp6OgoACXLl2CyWTy26Pm/dlms6Gurg5xcXFYvHix2EUmRhGm5FWpVFiwYAGUSiVu3LjhE/aLL74A0L+2oaOjA3fu3MGKFStoeGycw5S8ADBr1izMnj0btbW1vuibkpLimwr++++/4XQ6ad3ufwDm5OV53vcGzH/++QdutxsXL16E2+1Gd3c3ampqsH79+iEHlhDjD+bkBfpXm82ePRt//PEHOjs78c4778DtdqO6uhp9fX1Yu3at2EUkxgAm5QWAxx9/HE6n0xd9zWYzzpw5g1deeYWi7n8EZuXNyspCYWEhysvLkZSUhFOnTiE5ORmPPvqo2EUjxghm5QWA4uJi6HQ6pKeno7KyEq+//rrYRSLGEKblTUxMxPbt29Hd3Y1169bRyY//MSR1xGkkzJ07F3v37qVp4P8gnDDwIC+CiDJdXV3geR4ymQwcx4HnefA87/uZ4zjfm0vDeYMpQPISDMN0m5f4b0PyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLMQvISzELyEsxC8hLM8j9TSfMx6ItduwAAAABJRU5ErkJggg==)
Physics-General
Physics-
A double convex lens, lens made of a material of refractive index
, is placed inside two liquids or refractive indices
and
, as shown.
. A wide, parallel beam of light is incident on the lens from the left. The lens will give rise to
![](data:image/png;base64,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)
A double convex lens, lens made of a material of refractive index
, is placed inside two liquids or refractive indices
and
, as shown.
. A wide, parallel beam of light is incident on the lens from the left. The lens will give rise to
![](data:image/png;base64,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)
Physics-General
Physics-
The slab of a material of refractive index 2 shown in figure has curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P, as viewed from the left is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAACKCAYAAABPV20XAAAgAElEQVR4nO2deVyU5drHv8MMAww7soMioiKJoomkiYgb7q+5tIgdl7S08vRmZUfrlJ3TckrLtEU9pcc8leWumZq45BJp4q6koOwwgAjKzgzM8P7BZ57XcWZYFJhBn+/nMx/gnvt5npuZ5/fc933d131dktra2lpEREQsFitzN0BERKR+RJGKiFg4okhFRCwcUaQiIhaOKFIREQtHFKmIiIUjilRExMIRRSoiYuHIzN2ApnDkyBGUSiUjR47E1dXV3M25b8nOzmb37t0AyOVy+vbtS2hoqJlb9eDSZkR68+ZN5s+fj1qtxtvbm8GDB5u7Sfclv//+O//+979xdHTEx8eHzMxMcnJy8PX1xc3NzdzNeyBpMyJdtWoVbm5utGvXjpSUFFGkLUB6ejqvv/46MTExzJs3Dzc3N5RKJXl5eVhbW5u7eQ8sbUKkf/zxBytXriQuLo5169Zx4cIFczfpvmT9+vVoNBpefvllnJycAPD19cXX19fMLXuwaROGo08//ZT58+fTtWtXQkJCSElJMXeT7kt27drFkCFDBIGKWAYWL9ItW7aQmprKs88+i5WVFb6+vpSWlnLjxg1zN+2+Ii8vj5KSEoKCgszdFJE7sOjhbnZ2NqtWrSIjI4Nu3boBoNFoaN++PSkpKbi7u5u5hfcPVlZWyOVySkpKhDK1Wk1VVRUODg5YWVn88/y+xWI/ebVazbZt2+jTpw+XLl1CqVSiVCpJSEigW7du5ObmmruJ9xWenp5MnTqVt99+m5MnT3Ly5Ek2b97MZ599Rnl5ubmb90BjsT1pSUkJFRUVjB49Wm9N1NHRkf79+4vWxhZg0aJFFBYWsnTpUgA6d+7MSy+9hKOjo5lb9mAjESMziIhYNhY73BUREalDFKmIiIUjilRExMKxWMPRjRs3OHz4MDt37iQ+Pp6qqipzN+mBIzo6mg0bNhiUf/HFF3zwwQd6ZeHh4fzjH/+gd+/eeuWFhYW88847bN26Va/8448/5sknn0QqleqVHz9+nHfeeYeLFy8KZXZ2dmzcuJHw8HCj7TTWnvHjx/Pmm2/i7+/fqPa8++67TJ8+HZlMXxKm2rN+/XoiIyMN2rJ+/XoWL16MWq0WyqKionjvvffo3Lmz0fY3hMUYjmpraykvL+fgwYNs2rSJhIQEAgMDiYmJITo6Gjs7OyQSifACkEgkwvrdneV3/l7f+4Deee78Wd9xup+Nfb+h90y939Dfd753t+U6EhMTefXVV/nll1/qrSfS8lhET1pSUsLZs2dZtWoVJSUlREVFMWvWLDw9PfVufBGRBxGzirSsrIy0tDQ2b97M3r17iY2NZciQIaIwRZqN/Px8UlJS9IafDg4OdOvWDQcHB726mZmZpKam6pV5enrSqVMnbG1t9cqrq6u5du0a+fn5euVdunTB19e3We9fs4n0+vXrbN++nSNHjuDt7c27776Lt7e3uZojco/k5eVx+vRpCgsLhTKZTMbw4cPx8PAwesylS5c4c+aMXllQUBC9e/dGoVDolVdVVXHq1CkDEUVERNC1a1eTbospKSls2LBBz90xICAADw8PA5FeuHCBTZs26ZX169cPT09PA5FWVlZy9OhR4uPj9cqffvppvL29Deba94JZRJqbm8v69es5f/480dHRhIeHi76hbYw7TRkVFRWkp6ejVCqFMmtrayIjIw3q6igsLCQpKUmvzM7OjtDQUINjampqyM3NNajfpUsXamtrTV6jf//+9O/fv1H/w5gxYxgzZkyj6jo6OvLcc8/x3HPPNao+NGwHMEWrG46USiXr1q3j6tWrxMTE0KVLF8GidqeRx5TBRzQcmT7mTlrKcGQh9sY2xd2KtFV70vz8fNauXUtqaiqjRo0iMDCwWYcFIiL3I60m0rKyMrZs2UJycjKTJ0/Gz89PFOh9hqX3rmq1mo8//piNGzfqlc+dO5dp06Zhb29v9LgjR46wdOlSsrKyhDJvb2+WLFlCWFiYXt2NGzeydOlSqqurhbJ+/fqxaNEiOnXqdFftbpXhbm1tLadOneK1117j+eefJzg4uN5hmDjcbXvDXXMLVK1W8+abb7J27Vq98tdff5158+YJRqLKyko9Sy+Ara0tcrnc5GdSXV1NVVUVWq1WKLOyskKhUBh0NLo9uLd/HjKZzGjdxtIq1pqSkhKWLVvGiBEjCAkJwcrKql4xilgee/fupXfv3ri4uODi4oKrqys9e/asN96UWq1mwYIFuLm56b2WL19uco9qfHw8gwcP1qvv5+dHQkJCve2Ty+UsXbqUoqIivdfChQv1rLh2dnY4OzvrvWxsbOq996ytrXF0dNQ7xtHR0ajo5HI5Tk5OenXt7e3vyTDa4j2pWq3mvffeIy0tjddff71Jx4o9qdiT3i/cSyfU4nPSo0eP8u2337J69Wqxp3xAUKvVJpdFmvLQaMpDqTHHN/ReSz9oLFKkZWVlLF26lNjYWANHZ5H7l+LiYmpqagDTYqrvZ2NsErop053lt/9t6pqmftdoNHptvXHjBidOnDAI1TNixAg6dOigV5aRkcGJEyf0nCbs7e0ZOnQoXl5e9X1cDdKiIj106BBqtZonn3yyWZwVxJ64bdBWh77GHCiKi4spKCjQK9eNFG5HpVJRVFTEzZs39cqqq6upra29p3u3xURaWVnJ119/zZQpU7CxsWmpy4iYgZ9//tnAfW7AgAFMnjwZV1fXNm0EvF18np6eTJkypcF6UBcPytRWtHt9aLWYSH/99VdsbGx4+OGHW+0LmzVrFgsXLqRr166tcr0HlZ49exqsKXp5eRn427Y1WnIEcC/nbhGR1tbWsnHjRqKjo3F0dGw2v1yNRsPBgwf58MMPgTr/yfnz5xMdHQ1ATk4OZWVlzXItEdN06NCB9u3b65W11SFuW6BF1kkvXbqEVqulR48eyGQyk8aApr6++uorPvroI1auXMn+/fuZMWMGiYmJQjR7qVRqcseFSOtR33doTmqqStiy8GG+PG38/draWqqqqpg/fz729vZ6r48//piysjLBal1QUMCsWbMM6q1cuVKYh97+uhdapCc9ffo0vr6+ODo6NtsXEx8fz9q1a/nhhx8IDg4GYNKkSXp13Nzc7mtXw9raWioqKigpKRE+VxcXF2xtbc0uAKjbTlZaWopGo7GI9txJ6cXV/OenakZONl3HxsaGZcuWsWzZsnrP5e7uzpo1a1izZk0zt9KQZhdpdXU1iYmJdOzYEQcHh2b7slavXs3QoUOFdBPG+O6775rlWpaIVqvlypUrbNq0ib179yKTySguLmbatGk8++yzFpFyIyEhgRUrVvC3v/2NgIAAczdHn+JM9p7yZKTxnWjAfTQnzczM5NKlS1RUVAB1LlPjx48X3k9LS6O8vJz27dsjl8vvumG3U1VVxYULFxg7dmyTRG+JT/O7RalU8vrrr9OjRw8OHDiAk5MT58+fZ/bs2QQFBTFp0iSzjyIGDhzIwIEDKSwsNFhzNC8VpP76AxV9XsAn9RNMJSix1Hl1k0W6Y8cO9u3bR8eOHbGxsWHPnj3Y29szbNgwAP7880/s7e3x8PBoNpHcunWL2tpawbzfFO4Xof7www/Y2Njw5ptvCmkfevXqRWBgIDk5OWi1WrOLVIclzD/1yDlPnPU4nu0J2zebuzFNp8kivXbtGqNGjeKZZ55BoVCgUqnYvHmzINLU1FQcHR1p165ds1l1XVxc6NSpE7t27RJ2zusMRv3792+2HtuSWb9+Pe+++67RvCzNOfdvLiypPalxX7PruDPJ+zVcO56PVvMloc4zGNpVP3yKsZ40NTWVXbt2GUScmDFjht666J9//snPP/+sFz7G2dmZqVOnEhAQ0HrD3Rs3bpCbm8vQoUOFmC+lpaWCy19FRQXFxcW4u7ujUCia7YtydHTkvffeY86cOcydOxcADw8Pxo0bh0wmu+9DrxQUFJCTk2Owd/HatWvk5OQQEhLSar3ovn37+Oabb/T2S/bu3VuI7giW15M69ZvCcy4lqFVVSDN2Ud4lFH8X4wm/jIVJ6dGjh54boFQqxcnJSa+uq6srvXr10tvdY2dnh4ODQ+tad9PS0rC1tcXb2xsrKyt+/PFHDhw4wO7duwG4efMmNTU1uLq6NrtwwsPD+fbbb4W9gE5OTvj7+z8Q2dUqKiqQSCQGwbB27NhBt27d6NSpU6uJonfv3rRr105vzuni4oKzs7Pwt6WJ1D1kOONDQKMqRXLmI3L7DiLY07iD/Z2CateunbAOb6y+Di8vL5M+uq0q0hs3bggGHGtra8rLy0lKShLWJgsLC9FqtXc1d2wM3bt3b/ZztgX8/f3x9PRk+fLlQlrCdevW8e233/LJJ58IPVhr4OnpiaenZ71b1SxNpDpkNo6Me+sQWrvWv3arDXeTk5OJiYnh1VdfNRp+s6ioCI1G02IifVCRSqUkJCTg7e3Nl19+CcCQIUP47rvv6NGjh5lbZ4ilihSJBFsn084uzeF40BI0WqTFxcWkpKTg7++Pi4uL0TpFRUV3bYUVqR9HR0dh2UuHpX7GFivSBmiMSIuLi/V2ukDdljRXV1eDPDJ3nvtuabRINRoN/v7+dO/e3WBupEM3aW5OJwaRtkV+fj7W1tZ33LDVlOQXUqaS497BDQrTSFW50dXHGSsLuk0aI1Kd4ex2oqKimDlzZotNOxotUjc3twbDn1RXVyORSOoN6iRy92i1WgoKCjh79iwajYZevXrh4+NjMeujUBcxPjAwUN+gpyrgj327uKzqybTn+qDctZp1dlN4b3IvbGVNdU6ppjD1ImcvXKVQddtmbisZLqFDGNvz7oWybds2IXufq6srERERuLq66tWZPHkykycb9yusT+AWsQtGq9VSU1ODTCZr8ZtGpVJx5coVzpw5g1QqpW/fvnpBtpsTS3rYlJaWsmHDBo4ePYpEIiE8PJxnnnkGHx8fczdN4NFHH6WiokIvsl5lQS65Fbk4hz+FW2UaG/90pP80X+TWVjT105VIaqkqLiAr9So5FbdFV5DJ8fTVj1S/Z88ezp8/32ColSlTptCpUydSUlKEKYW3t7fBkpe5qPeurqmpYdeuXezbtw+oC9n/2GOP4ezszEcffURaWhoSiYRevXoxc+ZMqqurOXjwoLDwO2HCBB599FFqamr48MMPKS4uRqFQMHr0aB599FGSkpL48ccfKS4uxtramtmzZ9OlSxfOnj3Lli1bqKysxNHRkXnz5uHh4cHvv//Oli1bqKmpoaysDIVCgUajIT4+XojI5uPjw4IFCygtLSUuLk7I1REdHc3w4cOxs7Nj6dKl5ObmYm1tzcCBAxk7diw5OTn8+OOP5OTkAHXO+wMGDCA9PZ3//ve/3Lp1C7lcLrQxNTWVzz//HIlEgqenJ5MmTSI4OJhDhw6xf/9+KisrsbW1ZcmSJajVao4dO8ZPP/0EQI8ePZg4cSIeHh6sWrWKxMREJBIJISEhvPjiixQWFrJp0yYuXbqERCIhJiaG8ePHU1BQwO7du3niiSeQSCTs2LGD6OhorKys+Ne//oVarcbR0ZHJkycTERHBqVOn2LFjh7DA/q9//QtnZ2fOnz/PV199BUBgYCBPPPEEgYGB7Ny5k7i4ODQaDUVFRXd9U+nCm9ShokCppCynHZHT2lF+7WdS3IMZ5O2MzKrpIgWoUVVQfLOQG6W3CU4mR15Ro1fPwcEBd3f3BuMf6Xr9V155xaDHu/1hYy7qFamVlRUPPfSQEFnB399fmI9GRUXRs2dPoG6NSKPRCNvTYmJiAOjYsaPQqw4ZMgSVSoW1tTUBAQFIJBI8PDyEcqlUKnygvr6+xMTEUF1djVwuF+a4AQEBjB49mpSUFA4fPkx0dDRKpZIjR44wbdo0IQmPbk0xNDRUWL8LCAjA2toaiUTCwIEDKSsrQyqV0r59eyQSCc7OzkRGRlJaWirUl0gkuLq6MmTIEKqqqpBKpbRr1w6oG/6PHj0aiUSCQqEQHNw7depETEyMMKqAOutsUFAQY8aMEUSt2yAdEREhBE3WnUOhUOiV635aW1vj4OBAfn4+UqkUqVSKjY0NDg4OjBkzBo1Gg1wuF5xL/Pz8GDZsmDCE0+V49fHx4X/+538AhPCcACEhIdjY2KDVasnMzGTHjh1NvJ3+H50IakqLuHjyCMn2oxgnzePXo0fQtBvBxVMphIwKRSZr6qjLGtcOoQwY7kio+raYRlZSHILc9GpGRUURFRXV6BhH98qxY8f473//qxfnqGPHjjz//PP1bgxpiGYL6VlaWsq6deuoqalh5syZzXFKk1y/fp0ffviBPXv2IJFImDBhArGxsUZd5loKU1+8qQBbxsoaumnuvHlUKhV79+5l5cqVqFQqZs+ezYQJE3BycjJ5ozW1XMe9hPT8/6zsWm7lneTL+a9wNM+fJxZPpWbbf/j3ZVfmfvoOz3QPQNYMAqkvYJnu79t/mvr95s2bRueO8fHxfPbZZ8IoC+o6pn/84x+EhoYKZcXFxVy/fl0IwgZ1gbd9fHxwdXXFzu7uFmibbRInlUqxsrJCrVa3+DzO09OTF154gdmzZwN1ewB1m8vvZ2xtbRk3bhz5+fkolUpiY2Nb3eNq7dq1vPHGG6hUKqFs2LBhLFmyhI4dOwK3CUCroargKi6Tv2X7SB9ktnIk/WKYqgEbhS3WFubOacq6GxERwZo1awwi2NvZ2enVd3JywsnJqdnb1WwilcvlyGQyqqqqWlwsEokEGxubBzLAmUwmQy6XY21tbRaXyFmzZjFr1qwGPY4AalSVnNzyG51enI6DbpBjLafuW9OiLi+lSgM29k7YSGvR1NSg1VohtapBpbXCxtq6VZdoTIlUKpWazBPT2IHovQxYm+1Rprt5VCqVRUy272ccHR1NOpRYArqhpjb3F5RM5BEfY6FUCtj1+hj69+7MB7/VoFUrObDpP/z3hzNkJ3zDP789Sk5xTZPC69SHuiidxMREkq5mU1pjvM6dIU+a+3W3NOuahS6Mh1qtvuvxt0jDDB06VG/eY2noBGPbJZZ575uq5cPjq+JxWdiJVUlJXLc7z+49v+AU0we5zyMMs/HDVSHnbgZlBoKtzCF+4wqW/XwVjdqJ0UtX89LDhg+5o0eP6g3j3dzc6Nq1q8leFOpsMcnJydy6dUuvPCwsrNmiZTS7SKHOwNHWwztaMm5ubg1XaiVKSko4fvw46enpQtnEiRMNnABM0blbHxIvHuWCRInCPwL3kkyupHrSobscezvJXS3RGFCZzY2H/sauZ535Y908PjunNCrSgwcPCtZ9qMsi7uvrW++9XFxczMmTJ0lJSdEr9/HxEVYCwEKcGQBhD2llZaVeA0Wal3PnzlFaWkpUVJS5m4JGo6GkpITCwkLhRtRtY2uMbcLDzYOyy5fIHTqZvtVx7I8/Rpeec/F1bYd1c81H3R7h8UGgrbmOynUQz4S1N1pt8eLFRsO+1Dd98/Hx4bnnnjP6XnNN+5pVpLqn582bN8XcLy3IuXPnUCqVFiFSV1dXHn/8cb2eQqvVNtp4KPMLYPjQKGIGdebarQv4dvKke49AXOyb22J0ibWzFrPppjOz/jHeaI2W3AVjMT2pLq5RYWHhfb8cYk60Wq2FBfq6e+xCZ/BesC8dnKpxHj2N7sNtaedpeg549/gxcNocSje8y3++/IX+/5lC4B012vxWtcYgirR1sPQA4E3Zqia196NudVWOi/u9ZR+rHzdChg7BzjGb3HeuYyyFsaX2pM26mqzLhlxUVHSb14lIczN27NgW9+q6L9FoqMhM4s+R/TEW4+PQoUNotVqjr+3btxMeHk5gYKDwGjt2rJCtoaE6FjPcBfD19SU1NZXS0lJxGaaF0Gg01NbWmi1K4hdffMEHH3ygVzZp0iQWLVqEt7e3xW36Vm6dR/SCnyjXyun60vf8+kqE0XqDBg0yaewZP368Xnzpu61zNzS7SAMCAjh79ixFRUX3nDxVxDinT5+mpKRE2MjQ2sybN48XX3xRr8wS53I6fCd9QfKkLxqsp+sRWwKLGe4CdOvWDZVKRXZ2tuh5dBc0pgdKTEzkxIkTrdCaB4sHwuMI6kIgBgYGkpycTL9+/VrE4VhEpKWwxBFBi2RVi4iI4Ntvv6WkpEQvHqtI8xASEoKvr6+5m2ESS5uTNoWWsvBaVE8KdX6Lq1atIjMzEz8/v/s+wnx9HD58mNWrVwN1cYNnzJhhkIAXIDs7m9deew2oC90xc+ZMk+E7evfubdFTCd0NeefP+urUV27qfHfWMfW+7rO6vfzO32tra9Fqtfz000/ExcURFBTE7NmzBb/dhIQEtm/frpek2t/fn9jY2BZ33GkRkTo4OBAWFsaRI0fo27fvA7mlTMcrr7zCV199RWFhIRs3buT777/nf//3f/X8QSsqKnjllVfo1KkTkydP5qeffmLVqlUsXLiQwMA7l9wxGa3RkqhPNMbKjP00Vab7e//+/axatUrPuT0oKEj4LO8U6TfffMOmTZv02jB69GiefPJJIWBA3759CQgIQKFQIJfLhWODgoKIjY3V29hgZ2eHm5ubUOfYsWOsX79eLzJDYGAgzz///D35W7eISAGeeOIJJkyYwF/+8he9PBqWyuHDh9m6dSsLFy7Ez8+Py5cvM3fuXDZv3nxPoRp/+eUXvLy80Gq1ZGRkcPr0aSE+k46TJ0+SnJzM+vXrUSgUSKVSFi5cSGpqqlGRbt26lfz8fAMLa2thbAkmPDycxYsX07t3b4P6GRkZ/POf/yQuLk6vfM2aNUKiL6gziL333nsGRrHvvvuORx55xOC8kZGR9OzZE61WK4hXJpOZjNAxadIkRo4cqSd2W1tbve/Cx8cHb29v4ZxQJ2ZnZ2eTUzddvfDwcEJCQvRGObr2WNxwF+qWYiZPnsy///1v3n/f5H4li2H//v34+PgIX/COHTsIDQ01KdDt27czdepUvTJXV1c+++wzvQzkumWoqqoqbt26haOjo8H6cWZmJv7+/sLN4uHhgUKhQKlUolarDdZDi4uL9bJ3tTZNXYIJCAhg7dq19fakUDcd2LBhg1Be33AZ6kYUulFaY6ypDg4O2NvbG61ravrQlDlqfYEILFKkANOnT2fgwIE8//zzRudhlkJ+fj4ZGRk888wzODs7U1NTw5EjR3jjjTdMGkAmTpxIZWVlo86v0Wg4deoUly5dYvbs2QYW7zs3Ltvb2wtCNmaE0QUhE2k9zGn1bVGR+vn5MXfuXJYsWcKyZcssNgPauXPncHR0FHq9c+fOcfXqVQYNGqRXTxd1wtbWlsLCQhITE/Xel8lkdO3aVc+3tra2lgsXLvD9998zePBgoxm6dBEtdJSUlKBWq7G1tTVqdOvcubO4FbCFyMrKIicnR68H9fDwMAhCXl1dTVZWlsGIpkOHDnh6eho8WC22JwX4y1/+wlNPPcWxY8cYOnRoS1+uyVRXV3PmzBlcXFzw9vZGqVTy5ZdfMmLECJKTk/Hy8sLFxYXCwkKuXLlCTU0Nffv2JSMjwyDdgL29PdOnT9cbIsfHx7N+/XqCg4OFwGkAv//+O7W1tfTr14/g4GCysrLIzMwkICCA1NRUHBwc6NKli9EH28CBA1vuA7nPyMjI4Ny5c6hUKkF4zs7O9OnTx+gc89KlSxw8eBD4f2H169cPNzc3FAqFUFZVVcWpU6c4d+6c3vFjx46lXbt2BiMdixapj48PixYt4vvvv8fX15eQkJCWvmSTyMvL4/Lly2RlZfH555/j4ODAyZMnCQoK4vDhwzz22GMA5ObmcuzYMQICAtBqtYSHhxuI9E6Ki4t59dVXKS4uJjAwkA8++ABXV1dGjBjBmjVr0Gg09OnTh4ceeojo6GjeeOMNunfvTkZGBhEREUaNRlCXVFitVuPn59fsn8fdkpmZyYEDB8jLyxPKrK2tmTJlisk13RMnTnD48GHg/2/i7t27M2jQIIOQJRUVFfz66696o5fa2loGDx5MWFiYyWlJaWkp6enpVFRUCCL19PTUC8V5O6NGjWLkyJF6xihj81aFQsGkSZP07A+305xLZC0uUqiLyXP58mW+/PJLFi9ebFFbrdLT0+nUqZPQOwUFBdGjRw+USiWRkZHCELh9+/Y88sgjwobrLl26NLhgb2VlxaxZs/TKnJycsLa2Zvr06Wi1WqytrbGysuLtt99mz549QJ2zwqOPPmoyBMmJEycoKCjgmWeeudd/v9mwtrbGxcVFb4lCJpPVm/rDzs7OYNju6OhodIhvZWWFg4ODUF8n6oaWo0JDQ3nooYeEY5rLVe/28zW27t3SKiKVyWRMmDCBZcuWsXPnTmbPnm0RHil5eXkkJiYycOBAhg8fXm/dgoICbty4QU5OjhDjt6H/wcnJiTlz5hh9785lqfbt25usa6wt2dnZFvEZ6vDx8WHixIl6ZQ1ZZ8PCwoQsCA05QNja2hIVFcXAgQPrXUs1B425tsWLVCKR0L59e6ZMmcKaNWvw9/dn1KhRrXHpeklPT+fq1atMmDChwbr+/v64ubkRFRVlMr+IyINLQ72qxYsU6pYNIiIiqKqqYu3atWi1WkaOHGnWpYTw8HDCwsIa5cFjZ2dnMftjo6OjDRIKi5iPhtZadXXullYTKdQJdfDgwQCsXr2ampoaYmJizHbzNzRnslSCgoJa/ZrV1dVUVVXp+cFaWVkJHlKmqKys1Fte0nn5mNqwrtFoqKysFDa2647RZc2rj6qqKtRqtV4bddH+b6+js/Tq6jSUDeDYsWN8+umnZGdnC2VeXl4sXrxYzwB14MABAzfFzp0789prr93Thgiz3KGDBw9GIpGwatUqrl27xpQpUyzKUmnpFBcXU1NT06prpfHx8SxZsoSsrCyhzNfXl08//dSkxV6tVvPpp5+yceNGvfK//vWvPPXUU0YfzufPn2fZsmVcuXJFKLO1teWLL74waZGFuofIypUr2bZtm175jBkzmDx5MgqFgurqatCxNCcAAAz+SURBVL766it27twpvF9bW8vTTz/NxIkTTXYWAwcOJDIyUs9V8Hbrr45hw4YxdOjQZp8fN1tWtbshPj6eFStW0L59e8aNG0dISIgYzaERfP/99+Tm5gq7ZlqCe8mqdmdZSznYm9rNcme923tWU68765hagjEmUt3vxo7R0b59+7v2ujPrWG/AgAF0796d3bt3s379ejp16kRkZCTBwcF4eHhYrIeSuamsrKS83Fi8OxFLormsz2afkLm4uDB16lQeeeQRDh06xO7du4mLi8PZ2Zng4GC6detG586dRcHehkKhwMHBwdzNEGkk97oma9bh7p2o1WqSk5PJysoiKyuLvLw8bty4QUlJiVnXwSyNzMxMqqqq6Nq1a4td49atW6hUKpPD3Tu527VCU8c1VLe+4bap90zVacwwXPd7U4fsup/29vZ3/WC1KJHeTlVVFYWFhRQWFnLr1i2LjkRwv+Lm5iY4G4iYD4sVqYhp0tLSqKysFNzdRO5vHtzgQ22YX3/9lS1btpi7GSKthCjSNsjtSwEi9z9mt+42BqVSKWzEhbqdEl26dGmT3kLNgbOzc6OjQoi0fdrEnPTll1/mjz/+wN/fn4qKCsGTpT4PlPuZlt5Pevr0adLS0oS/vby86NmzpxhD2Uy0ia7o1KlTvPXWW4wePZrs7GwWLlzI+fPnH1iRtvR+3Lfffhu5XE5gYCDl5eUUFBQwatQonnzySTEjgRmweJHm5eWhVqsJCwtDq9WSkpJCRUUFwcHB5m6a2Th79iylpaUtlun77Nmz7Nmzh169elFRUcF3333H7t27CQ8PNxqyU6RlsXiRnjt3jps3bzJv3jykUinl5eWMGzeOHj16mLtpZuP8+fMolcoWEWlycjL29vbCQ1ChUNC3b1/i4uL0oreLtB4WL9L09HRhqCWTyTh79iwHDhxg3LhxFh0mtCWpqamhurq6Rc599OhRunbtqrcjRKVSoVarW+R6Ig1j8UswZ86cISgoiIiICB555BEeffRRrl27Rn5+vrmbZjYcHBxabG6YlJRkEMo0LS2NgIAAi04SdT9j0SItKCjgypUrdO7cGa1WS2lpKR9//DHh4eGEh4ebu3lm46mnnmL+/PnNft7a2lri4uLo3Lmz8PfVq1fZunUr/v7+okjNhEUPd8vLy3F3d+ell14C6iLGRUZGsmbNGjO3zLxUV1cLUQeak8zMTFJTU3F3dyc1NZWcnBxWrlyJl5cXU6ZMsZjwMQ8abWKdtLkpKioiMTERf39/IbZtdnY2GRkZwlxPKpXSu3dvi9wSlpCQQHFxsV6yo+bg6tWrvPTSS1RVVQF1uU0mTZrEs88+26zXEWkaFt2T6khKSqJz585CLB2tVktRURFlZWV4eXk16Ql/+PBhzp8/z4YNGxg2bJiQTGrLli1s3LiRDh06CDF42rdvb1aRlpaWUlhYSIcOHfTi+5w/f56cnJxmF2mXLl3Yu3dvs55T5N5pEyJdsmQJn3/+OQqFgps3bxIfH096ejrdu3dvcpwfpVKJk5MTI0eO1AvkDDBo0CBee+013N3dGzzPyZMn2b9/P3Z2dkRFRRESEsKJEyeorKwkOzubwsJCBg0ahK+vLz/88AMKhYIBAwYQERHR6LZWV1eTlJTE9u3bGT58+APrvPGg0yZE+scff1BaWkpcXBy7du3i+vXrTJo0id69e5vMRWmK2NhY1Gq10XSM8fHx5OXlYWtry9ChQ3n88ceNniM+Pp433niD2NhYysvL2b59OyqViq+//pqKigqGDBlCcnIyu3fvpkePHoSGhnLy5EnS0tIIDQ3Vy4dZH25ubjz88MMcP36cl19+mcjISJ588km6du3aqAeJyP1BmxApwOzZs7l8+TKZmZk4ODhw69YtNm/e3OBxsbGxBnlEjfHYY48RGhqKWq0mPz+fv//97zg7OxMTE2NQ98MPP2TEiBHMmTOHyspKUlNTyc/Pp7q6mpEjRzJt2jQ2bdrExo0bWbJkCQ8//DDV1dVcvHjRIAzM448/3mAM3aKiIk6cOMEff/zBwYMHmTRpEk8//XSD/5PI/UGbEenbb7/Nhg0bWL58OX5+fvztb3+jY8eODR7X2CzdHTt2FM6nVqvZt28fe/bsMRBpQkICFy9e5OuvvwbqgmZ3796d5ORkXF1dGTx4MA4ODly/fp0JEyYQGRkphH8JDg42EOk///lPNBpNvW07c+YMiYmJuLm5MXHiRMaPHy+mPnyAaDMiDQ4O5sMPP+Sll17igw8+4JtvvmHZsmUGOVWaA7lcjpubG25ubgbvlZeX4+3tbWBQKioqwt7eXlhL/O2334TcKOXl5aSlpRlNKd9QlrkzZ86wYsUKFi9eTGxsLO7u7hw6dIjjx48TGxt7t/+iSBuiTYh0yJAhyGQybGxsCAwM5Ouvv+by5cskJCQgl8vx9vZu9LkqKiooLy9HpVJRU1NDaWkpBQUFbNu2jaioKIKDg0lISGDr1q3ExcUZHC+TycjPz+fChQsEBwdz8OBB/P39SU5Oxt3dHWdnZzQajeClA3VudWVlZXTr1q1J/3daWhppaWnExcXp9ZwjRoxo0nlE2jZtQqSfffaZQVlISMhd5Tp94403hCSxUOfA//LLL2Ntbc2LL74orBHGxcURFhZmcHxkZCQzZszghRdewMrKijlz5jBgwADc3Nzo3r07UCcuXapEqEudoFarmxz4OzAw0GSOUpEHhwfSmUFEpC1h0b67IiIiokhFRCweUaQiIhaOKFIREQtHFKmIiIUjilRExMIRRSoiYuG0CWcGc6HRaMjNzUWpVAJ1fsB+fn6C/+3JkyeBOi8kX1/fJnk+WQparRaJRIJEIjF3U0RMYPEizczMxMvLCxsbG6Au7k5paSk3b97E3d0de3v7Frt2QUEB77//Pjdu3KC4uBgPDw8WLFhAz549OXToEC+88AJhYWGoVCqCg4N55ZVX8PHxabH2tAQajYbr16+jVqvx9/fX2wBQVlZGSUmJGNvIzEjfeeedd8zdiPpYsmQJwcHBuLi4UFFRQXx8PL/++itqtRofH58WjbtTVlZGcXExH330EcOGDWPHjh3Y2tri5eXFhAkTWLZsGW+99RahoaFs3boVKysro8GjKysrOXz4MD/99BPp6em0a9cOtVrN7t27KSsrY/PmzVy8eBG5XC4E/rp27ZpRR/7mRiqVkpeXx759+7h8+TIymUxwX7x48SJ79+6lX79+LdoGkfqx+J709OnTFBYWcvXqVXbv3k1SUhLDhw8nPDzc6C6V5sTb25s5c+YAdUmSdIK5fPkyGo2G8ePHA+Dj40NAQABJSUmoVCqh14e6GLk7d+5ky5YtDBgwgFOnTiGVSlEoFLz99tuMGjUKX19fdu7cyY4dOwgLC0Mul7Njxw5cXV0ZNWqUEDampejatSulpaWsWLGCH3/8kVGjRjF06FBu3LhBYmJii15bpGEsXqQAb731FpmZmSQlJWFnZ0dVVRW///77PZ83LCyMv//9742qe/z4cbRaLT169ODWrVt6cW9tbW1xc3OjsLAQtVqtJ1KVSsUXX3zBCy+8QGxsLJmZmajVamFny+TJkwkPDyc3N5cjR44wdepUnJycOHPmDBqNxuRccdOmTY3a9N4ULl26RHJyMqdOnWLv3r0PdJYAS6JNiHTGjBmcOnWKS5cu4e7uzuzZs4XYsPdCY7OEXbt2jU2bNjFo0CAefvhhDh8+rPe+RqNBpVIZPXb//v0UFRUxYcIEAGH/6/LlyxkxYgTh4eFotVpUKpUQHeLy5cuCIer2AGS3M2DAgEZtem8KW7ZsYfny5XTu3JnIyEi8vLxISEho1muINJ02IdKHHnqIMWPG8OKLL/LJJ5+wbt06Vq9eTVBQUItfOzMzk/fffx8/Pz+mTZuGra0tHh4eZGdnC3UqKytRq9V07NjRYA5ZXFyMv7+/wdw5NTWVUaNGIZPJqKio4OLFizz22GMAZGRkIJVK652P+vn5NWvqw61bt5KSksKiRYuYOXMmXl5eHDlyRBSpBWDxIh0+fDguLi4oFAo6dOjAihUryMzM5NixY8hkMmFjdUugVCp59dVXCQoKYvHixUDdHLNPnz7IZDKWLVvGX//6V65cuUJSUhITJkwwOjzNyMggKyuLyspKrl27hpOTE0VFRXTs2BErKys0Gg1ZWVmCZbigoABvb+9WC5GSnJxMSUkJn3zyCQEBAcL/4OHhIeyRFTEf4n5SE2i1Wn777TdmzpypVx4aGsrKlSupra0Vcqb4+PiwYMECwZB0O5WVlUyfPp3Tp08TFBTEokWLkEqlbNu2jQULFuDn58exY8d4//33+eWXXwBYsWIFKpWKuXPntko+0KqqKmQy2QObOd3SEUUqImLhiG6BIiIWjihSERELRxSpiIiFI4pURMTCEUUqImLhiCIVEbFwRJGKiFg4okhFRCyc/wOptwCsSow2dwAAAABJRU5ErkJggg==)
The slab of a material of refractive index 2 shown in figure has curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P, as viewed from the left is
![](data:image/png;base64,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)
Physics-General
Physics-
A rod of glass (
= 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of
light entering the glass slab through surface A emerges from the glass through B
![](data:image/png;base64,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)
A rod of glass (
= 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of
light entering the glass slab through surface A emerges from the glass through B
![](data:image/png;base64,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)
Physics-General
Physics-
An optical fibre consists of core of
surrounded by a cladding of
. A beam of light enters from air at an angle
with axis of fibre. The highest
for which ray can be travelled through fibre is
![](data:image/png;base64,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)
An optical fibre consists of core of
surrounded by a cladding of
. A beam of light enters from air at an angle
with axis of fibre. The highest
for which ray can be travelled through fibre is
![](data:image/png;base64,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)
Physics-General
Physics-
A prism having an apex angle 4o and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror
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)
A prism having an apex angle 4o and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror
![](data:image/png;base64,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)
Physics-General
Physics-
A fish rising vertically up towards the surface of water with speed 3 ms–1 observes a bird diving vertically down towards it with speed 9 ms–1. The actual velocity of bird is
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)
A fish rising vertically up towards the surface of water with speed 3 ms–1 observes a bird diving vertically down towards it with speed 9 ms–1. The actual velocity of bird is
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)
Physics-General