Physics-
General
Easy
Question
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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)
- 1.50 cm
- 1.64 cm
- 1.33 cm
- 1.86 cm
The correct answer is: 1.33 cm
Suppose the maximum height of the liquid is h for which the source is not visible.
Hence radius of the disc
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/862990/1/1184842/Picture6773.png)
![r equals fraction numerator h over denominator square root of mu to the power of 2 end exponent minus 1 end root end fraction](data:image/png;base64,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)
![1 equals fraction numerator h over denominator square root of open parentheses fraction numerator 5 over denominator 3 end fraction close parentheses to the power of 2 end exponent minus 1 end root end fraction rightwards double arrow h equals 1.33 c m](data:image/png;base64,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)
Related Questions to study
Physics-
A slab of glass, of thickness 6 cm and refractive index 1.5, is placed in front of a concave mirror, the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is 40 cm and the reflected image coincides with the object, then the distance of the object from the mirror is
![](data:image/png;base64,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)
A slab of glass, of thickness 6 cm and refractive index 1.5, is placed in front of a concave mirror, the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is 40 cm and the reflected image coincides with the object, then the distance of the object from the mirror is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAACHCAYAAAC71qMMAAAfhUlEQVR4nO2deWwc5fnHP7O73tO7vo/ER3wmTuw4iUninMQmpClngABRm1QCSikqVCqVKhUqVKT0oPQf2goVFVUUEJQ2BRogkBAS53Du+3CcxPcdX2vH6713Zn5/8NtpNiZAwtrZXc9HWimZXc+8s/udd555nud9HkGWZRkVlRhDc7MHoKIyHqjCniRMthuz7mYPQGV8kWUZj8eDw+HAaDQSHx+PRhP781nsn+Ekx+/309/fT1tbGx0dHTgcjkkxe6vCjmECgQB2u52BgQH8fj8jIyP09PTgdrtv9tDGHVXYMYjf78fr9TIyMkJfXx8+nw+NRoMgCIq4fT7fzR7muKLa2DHIsWPHaG9vp7i4mEAgMMamHhoaQqPRkJOTg04XmxJQZ+wYpLe3l7/85S/s2LFDEfaVL/hC3H19fQQCgZs82vEhNi/XSc6qVau4dOkS7777LiaTicrKyi/1hAwODhIXF0dKSkrMeUpUYccgZrOZRx55hNHRUbZv3058fDyzZ88eI15RFLHb7ej1ehISEm7SaMcHVdgxil6vZ926dTgcDmpqaoiPj6eoqAiNRhPi7vP7/QwNDREXF4fZbL6JIw4vsXX/UVEQBIHMzEzWrl1Lamoqn3/+OR0dHciyjFarVV6CIODxeBgZGcHv99/sYYcNVdgxjE6nY8aMGaxduxZBENixYwd9fX3AF8IPviRJwul04nQ6kSTpJo86PKjCjnH0ej0VFRXcd9999Pf3c+DAAVwu1xhPSSAQYHR0NGb826qNzRcROlEUJ/SYgiAo5sB4YzAYWLp0KX19fXz44YcUFxczd+7cMQ+TXq8Xp9NJXFzchIxrPJn0wg4EAnR0dDA4ODihx9XpdGRlZZGWljYhx7NYLHznO9/h/PnzbN68malTpzJ16tSQz8iyjNPpxGg0YjabEQRhQsY2HgiTfaGB3++nsbFRsT0nCp1OR0FBAVOmTJmwY8qyzIULF/j1r3+N2Wzm5z//+RhPiCAIxMfHk5KSEtWztmpjTxIkScLtdiOKIosWLeLgwYN88sknSJIUYmsLgoDb7cbj8UR1FuCkN0VikaBY4X/mRUdHB0ePHqW9vZ3y8nJ+9rOf8dprr5GXl8fChQvH2NvB/O1onbVVYccYQ0ND+Hw+MjIy8Hq9tLS0cObMGZqbm7HZbKxYsYLZs2cjCAL19fW899575Ofnk5mZGbIfv9+Py+XCarXepDP5dqjCjiE8Hg/bt29n+vTpOJ1Ojh49SmNjI1arlcWLF1NSUkJycrKS0ffEE0/w7LPPsmfPHu677z6MRmPI/lwuF2azOSpnbVXYMYIoitTW1rJjxw6amppobm5mypQprFy5klmzZpGUlKREGoMUFBRw5513UlNTw5w5cygtLR2zz2idtVVhxwCiKHLs2DFeeeUVTp48iSRJrF27lkceeYSCgoJr/p3RaKS6upoTJ06wa9cusrOzSUxMDPmMx+PBaDQSFxc33qcRVlSvSBQTzM7bunUrv//976mtrWVoaIjbbruNxx9/nLS0tK8NkWdnZ1NVVUV7ezt1dXVjvCSyLOP1eifojMKH6seOQj+2LMs4HA7q6urYu3cv9fX1iKKIyWQiEAig1WqxWq3ce++9VFRUfKUpIcsybW1tvPrqqwCsX7+ejIyMkM/o9Xri4+OjarVN9IxUBVEUcTqdNDY2cuDAAZqbm8nPz2fjxo1kZWXdUKRQEATS09OZO3cu27dvp7W1ldTU1BARS5JEIBBQha3y7ZBlGb/fr6SRiqKI2+2mtbWVo0ePKosDHnvsMWbMmPGtBWcymZg7dy6HDh2ivr6eWbNmhSw8kGVZyaeJFg+JKuwIRJIkBgcHaW9vp6enh46ODpqamujo6GD69OmsXbuWsrKyMe65G0UQBLKysigtLeXYsWN0dXWRkJAQErTx+/3o9XpV2Co3jiAIaDQaGhsb2bJlC6dOnaKnp4fp06fzzDPPUFFREfY1ihaLhVtuuYXDhw9TV1dHYWGhkkciyzKSJOHz+dDpdFGxPlIVdoQhSRLnzp2jtraWEydOcPnyZdLT09HpdDz88MOUlZWNi7A0Gg1FRUXMnDmTEydOsHz5ciwWi7IQQZIk/H5/SLg+klGFHUF0dnby0Ucfce7cOUpLS1m3bh0+n4/Tp0/j8Xi45557sNls43b8+Ph4Fi9eTE1NDU1NTUydOlUJ6gTtbL/fPybQE4mowo4AhoeH+fTTT9m0aRMVFRX89Kc/JSsrC4vFQldXFw6Hg+LiYvLy8sZ1thQEgXnz5jF16lT27NnDwoULsVgsSpZfUNgGg0EV9mQjOLMFAoExD1tBgQSDHn19fZw5c4YPPviAuLg4Nm7cSFFREQaDQfmcyWRi/vz5ZGRkTEj0L7ja5m9/+xsjIyPEx8cr7wXt7GgwR1Rhh4mgi25wcJCOjg4yMjLIzs7G7/cjiiJerxeXy4Xb7cbhcNDW1saFCxewWq2sX7+elStXYjKZQvYpCALJyckkJydP6LksXbqUP//5zxw4cIAHH3xwzDn6/f6I92lH9uiiBJ/Px8DAABcvXuT06dNkZGSQnJxMY2MjDodDeY2OjtLb24skSRiNRsrLy3n00UcpLCyMqBmwoKCAyspKPv/8c+67776Q9/x+Pz6fD6PRGNHmiCrsayDLsrLi5MtSNwOBAB6PB5fLRUtLCwcOHOD48eOIosiSJUs4fvw4Op0upMxB0MzIz88nLy+P7Ozscbebb5Q1a9bw3HPP0dLSQn5+vrI9EAgo5kgk+7RVYV8DSZIYGhqiu7sbSZJITk7GYrHg9/uV2dflcuFyuejp6cFut2MymfB6vbjdbrKzs8nIyCA+Pp5AIEBDQwO5ublYLBaSkpJIT08nOzs7YrPmKisrSUxMpKamJkTY8MUdKtKjkKqwr0HQnmxpaeHQoUMYDAYSExMxmUykpKRgtVqxWCykp6dTUFCAXq+nv7+fjo4OtFotNpsNh8PB0NAQ6enpJCYmEh8fT1paWkQLIojNZmPevHns37+fRx55JOQ9n8+nPBxHKqqw/59AIMDg4CCdnZ10dXXR3d3NyMgIXV1d9PT0MDo6SmpqKlVVVcyfP5+0tDT0ej06nU6Jxk2bNo3CwkLOnj3L4OAgJpMJo9FISkoKGRkZ6PX6iLZLr2bRokVs27aNS5cuhZSJCAo7kpn0wrbb7Xz22Wds27YNURTJyMhgypQpLFiwQDEtdu7cSUtLC3fccQcLFy4kOTl5zKwry7Jie7pcLnJycigsLESv1xMXFxdVgg5SUVGBKIqcP38+RNhBL08ku/0mrbAdDgdvv/02//rXv0hMTOSee+5h2rRp6PX6kFIEJ0+eJC0tjTVr1pCXl3dNN9exY8fYuXMna9asYfXq1Wi12oj90b8piYmJ5Ofnc+7cOZYvXx7yXvDBOlLPcVIIO2gvO51OBgYG+Oyzz5RFry+//DJ6vf5LFxo4nU50Oh133HFHyIwVTAoKBAKcO3eO1tZWKioqePrppzGZTFE5O38ZBoOB8vJy6uvrx6yiCd6dIpWYEbYoikpWXJBAIIDL5aK/v5+Wlhbq6uqoq6tj5syZvPjii5SUlCgraL4Mi8VCWVmZ8v9gMpDP56O9vV05bmFhIVOmTInoh6kbQa/Xs3DhQo4ePUpnZyfZ2dnKe0HPSKQSE8L2eDz09/eTkJCA1WrF5/MxNDREV1cXLS0tdHd34/V6yc3NZc2aNeTk5Fy3Z0KSJC5fvkx/fz9Go5He3l5SU1OZO3duxEfhbhStVkteXh7wRV+bK4Xt9Xoj+gEy6n8Rn8/HuXPn6OnpoaSkhN7eXpqamujq6mJkZASbzcasWbOYOXMmmZmZN+Rq6+/vx+Vy4ff76evrY8aMGVRWVir2eCxjMpmIj4/HbreHbA8+LMuyHJGmV1QLOxAIcPHiRf773//i8XhoaGgAvlgoO2XKFObOnUtubi5JSUnXPasGV4BLkkRfXx9Op5PCwkKSk5Ox2WwxO0tfjdlsxmq1jhE2fDFrq8IOM5Ik0drayjvvvMPmzZuxWq1UVVVx2223UVJSQlJSEhaL5YZmVI/Hg9fr5eDBg+Tk5JCbmwtAQkJCVARXwonZbCY5OZnBwcExReEDgUDEFq6MSmG7XC62bt3K+++/z65du+jt7aWoqAir1cq8efO+Vc3ps2fPUltby6pVq5g1axbJyclKEZlInJnGG5PJRGZmJi0tLTidTiwWi/Je0BSJRKJK2G63m02bNvHuu++Sm5vLnXfeyX333cfg4KBSmuDtt9/mgQceUGbZb4IoirS2tuJ2u7Fardx+++1kZWUpkcLJKOggRqORzMxMTp06hcPhCBG2KIqqsG8ESZLweDx0dXXx+eef8+abb7JgwQI2btzInDlzxpgZwS/5m5ofwYfB7u5uGhsbSUxMJC8vL+JTMicSQRAUMXs8npD31Bn7GxB00bW1tQH/e3g7e/YsDQ0NFBQU8I9//IPp06d/a9F5PB66u7sJBAJs2rQJm81GVVXVpHkgvF6CKQFXt8tTAzTfAKfTyYULF3jrrbc4c+YMvb29BAIBli9fzk9+8hMWLlz4rQIgkiThcDjQaDR0dnayefNmNmzYwGOPPUZfXx/Dw8NhPJvYInjBX+23VgM010CWZTweD3a7nba2NlpbWxXXnM/no6ioiAceeIDy8vIbzlsORgqdTidHjhzBYrGQmZnJsmXLSE1NRavVqqL+GoIz9tXClmVZNUWuJNg+oq2tjaamJjo7O/H5fKSkpLBgwQKys7PZv38/1dXVVFVVYbVab8j8kCQJu91OY2Ojkk+dlJREXl4excXFADHVjXa8CK4E+jJhRyoTLmy3283p06epq6tTcpbz8vKUfAudTsfhw4exWCzccccdpKSkXLeoZVmmo6OD+vp6MjMzEUURq9VKSUkJBoMh5qOF4SZ4t4xk0+NqJkzYbreb2tpa9u/fD0B+fj5Lly4lNzeX5ORkjEaj0iE2PT2dkpISMjMzr1vU7e3tDAwMYLFY6O3tpaysjOnTp6PT6SJ2GVakE5wIJq2wJUlSQqxBQdrtdnbt2sXbb79Nfn4+y5Yto6ysjIyMDCUyeKV4tVotxcXFX7va5Opj+Xw+/H4/L730EvPmzWPDhg2kpqaSmJg46aKF4Sbo/YimO13YhN3V1cUf//hH9u3bx7x587j//vsZGBhg3759JCYm8tRTTzFr1ixSUlK+0rshCIJSMOZaXLx4kd/+9rc0NTVRXV3N4sWLOXXqFNXV1fziF78gISEBg8HwtftR+WYEbetocoeO6WjQ399Pa2vrdbVnkCSJN954g3//+984nU60Wi1JSUnMmTOHu+++m1mzZoXVtn3xxRfZvn07fr+f1NRUVq5cSVVVFQUFBdcdXAk+2d+MB6Gr71aRyrFjx9i/fz/r16+nrKwMj8ej5NOE2zxZtmxZWPYTcglKkkRzczMffvjhdfUWl2WZTz/9FKfTiSzLiKKITqcjISGB+vp66uvrwzLYIDt27FAScgYHBzl+/DharZYTJ05c974MBgMVFRVK3vFE4fP5OHXq1DUXOUQS3d3dyLI8ZsYeGRlh27ZtuFyusB1rXISt0WiorKyksrLyunYSrDHxzjvv4HA4sFqtrFq1iueff56ioqKwDPRK2tra2L17Nz6fj7S0NNatW8fTTz9Nenr6de/rZvWgMZvNrF+/fkJ7qd8omzdvZtOmTWOEnZWVxR/+8IeIfCgPi9Gk0Wh44oknlNrOBQUFfP/73ycrKyscux/Ds88+S3JyMt3d3cydO5d77rlnTBs3lfARXN94tYAjefV9WIQtCAKzZ8/mV7/6FQ6HA7PZTEZGxpgii+Fi8eLF5Obm4na7sdlsSo0PlfAjSRKjo6NotdoxrUEi+TsP22OuVqslJycnXLv7SuLi4ibcJp6seDweent7iY+PDykpDER0AaDocUyq3BSCtQmTk5PH9IsMhtojEVXYKl+Jy+ViaGhoTO9HQRAi2sZWha3ylbhcLhwOBykpKSHbdTpdRLfsCHsoSZZlxbd86dIl4IsacDNnzlRD21GIy+VidHR0jLAjvedjWIUtyzItLS1s2rSJ/v5+EhMT6evro6amhmeeeSZsrdycTif79u3j4MGDaLVaSktLqaqqUl1+YUYURdrb2xEEYcwC6UjPkgyrsB0OB9u2baO3t5cnn3ySoqIiLl++zFNPPcXevXspKSn51i4ir9fL66+/zvnz56moqMDv99Pa2kp3dzdWqzWiZ5Fow+v1cujQIbKyssYEkuLi4iaPsDs7Ozl06BAPP/wwRUVFaDQakpKSyMjICNvCz507d/LBBx+wceNG5s+fjyRJjIyMYDabI/qLjka8Xi8nT56kqqoKo9Go5A8JgoDJZIroSSRswpZlWWlZUV5erohsZGSEvr4+li5dGpbssD/+8Y/ccsstLFy4UNlfuHqKq4TS399PW1sbpaWlIdvj4uIi2ocNYfSKiKLI5cuX0Wq1SsRRkiQOHDiAIAiUl5d/6yvc4XBw+PBh5s+fH1UplNHKkSNHMJlMzJo1K2S7wWCI+O8/bMLWarXKMqza2lo6Ozs5cOAAW7ZsoaqqKixRSZfLhV6vV0waURQZHR29rhRblW/OwYMHlWpYVxJsURLJhG10wXyR+++/n/fff589e/ZgMBiorKzk9ttvD0veSFJSEg888ABvvvkmBQUFuFwu7HY7ZWVlik2vEh4cDgcnTpxg/fr1Idu1Wm1UVJkN62VntVp56KGHqK6uBr6wxZKSksKWDKXX6/nd737Hxo0bef/99zGbzUo75ki296KRmpoaPB4Pt956a8h2nU4X8fY1jEOA5suSZcJJeno6L730krLeMdi1K9K/6GhCFEXee+895syZQ05OTkjFp2j5viP7fnINTCYTZrMZk8kU0fkK0cqFCxc4ceIEq1evDtmu0Wiiwr6GKBW2yvghyzK7d+8mMzOT8vLykNhDtNjXoApb5SoGBwfZv38/S5YsISEhAfhfxadgbZZouEOqwlZRkGWZ06dPMzg4yJIlSzAYDIqog2mqkRxtvBJV2CoKw8PDHDhwgIKCAqVDWLA0hUajifj8kCuJjlGqjDuiKFJfX09zczMVFRUkJiYqjVohuswQUIWt8v+MjIxw9OhRzGYzJSUl6HS6kEJCOp0uaswQUIWtwhezdUtLCxcvXqSoqIiMjAzgf52II30Z2JehClsFl8vFiRMnCAQClJaWYjabQ2ZrrVYbFb7rK1GFPckJ9ss8fvw4mZmZTJ06VdketK+jbbYGVdiTHpfLxcGDB3E4HCxevJiEhISQQp1arTYqq9aqwp7EyLLMuXPnqKmpoaSkRClCFBS1IAhRuzIpugwnlbAyMjLCZ599hiAILF++HLPZrJgfgiCg1+ujdnVS9F2KKmFj37591NbWsmLFCrKyskJMkGDj0mizrYOoM/YkpbOzk7///e8UFRWxaNEiNBpNyGxtNpsjuujk16HO2JMQu93Oyy+/zPDwMHfddRfx8fGKFyRYLjjYHyhaid6Rq9wQoiiyadMmdu3axQ9/+EMKCgpCRK3RaLBYLFHnt76a6B69ynWze/du3nrrLdatW8e8efMQBCHEBDEajVHrCbkSVdiTiHPnzvHXv/6V0tJSVq5ciUajCVlIoNfrY2K2BlXYkwJZlunt7eWdd95BkiTWrFmD0WgMWcuo1WqxWCyYTKao9YRcSXTfb1S+FlmWGR4eZtu2bTQ1NfHd735X6Q10ZT6I0WjEYrFEVQbfV6HO2DGMLMuMjIywc+dOdu7cSXFxMdOnT0ej0Sj9GYN1+Gw2W0TXu75eVGHHMC6Xiz179rBlyxbS0tJYvHgxNpstxATR6/XYbDbi4+NjZraGm2SKBDtRud3um3H4SYEkSezfv5///Oc/WK1Wli9frtS4vjJzLz4+HpvNFhMPjFdyU4Ttdrs5ePAg+/btw+l03owhxDzd3d28+uqrmEwmqqqqmDJliuLaC74sFgupqalRHWG8FhN+mcqyzMDAAJ988gkej4fCwkLy8/MnehgKWq2WrKysMa0oxptgIGQ8KSwsZOnSpUoJuCtNkPj4eKZMmXLdveejhQkXtiiKDA4OkpycTFdXF6dPn1a+4F/+8pfMnj2btWvXsnXrVk6fPs0PfvCDcRW+RqPBarWOafU2EYynoDIzM3n88cex2+1jRG0wGMjJycFsNsekqOEmCHt0dJTu7m7mzZtHIBDg4sWLLFmyBKPRyIoVK3j00UcpLi6mpqaGe++9d0Jm81j8cXU6Hfn5+eh0Ovr6+hS3XlxcHDk5OVGdufdNmFAbW5Ik+vr68Pv9VFdXM2PGDLq6umhvb0cURVavXk1OTg7PP/888+fPZ+XKlRM5vJhDp9ORmpqq3I3i4uLIysoiISEhpkUNEyxsr9dLfX29smB07ty5SvUhp9PJ6dOnKSwsxGKxjKmir3L9CIKg2NLJyclkZGSQnJwccx6QL2NCz7C9vZ3a2lqKioqoq6tjdHQUjUbD0aNHSUpKYteuXVRXVzM4OMiOHTsoLS2N2hUckYJGoyEhIQGj0agUlZwMTKiwW1pa8Hg8bN26Vdmm0Wjw+/0cPHiQsrIyvve973H27FkOHz6Mw+FQhR0GtFotZrP5Zg9jQhHkcPSo+4YEu4pdi5ycHGw2m9K/OyUlRRW2yg0xocJWUZko1Ow+lZhEFbZKTKIKWyUmCbtXZGhoCLfbrdSAA5Tc3xtNi5RlGVEU0Wq1IYEFr9fL0NBQSKey4Gc1Gs2ErtsLtrhISkpi8eLFSumwgYEBjEYjc+fOZdq0aVG9ljD4O2o0GuV3cLvddHZ2UlxcfDOHNgbtCy+88EK4dibLMkeOHOHEiRPMmTMHv9+P3W6nqakJt9uNzWa7oR/W4/HQ2NjI6OgogNI3sr+/nz179qDX60lLS8PtdtPb20tDQwMGg2Hck4yC+P1+tmzZwiuvvEJPTw/V1dXs3LmTzZs34/f7qaur49y5c8yaNWtMTkqwVffg4CBerxej0YjH42FoaAiXy8Xly5eRJAm3243dbsftdt+UHA9RFOnp6aG1tRVJkhS/eHt7O6+//nrERYnDPmPb7XZaW1vp6emhrq6OM2fOkJKSwooVK274x9BqtWg0Gj755BNcLherVq0iNzcXr9dLV1eXknp59OhRmpqaWLhwITNmzAjzmX05oihy6tQp6urqmD17NjqdjoGBAWpra1m2bBkPPfQQZ86c4YUXXqChoYHMzEzlewgEAjQ3N7N79276+/sxGo088MADXLx4kc8//5xp06Zx6dIl0tPTMZlMdHd3MzIywnPPPTemDfR4IwgCGo2GhoYGtmzZwuzZsykrK2NkZIQLFy5M6Fi+CWEXdiAQ4OTJk7z88svs27cPQRBYuXIlBoOBI0eO3PB+/X4/bW1tvPfee3z00UfccccdlJeX09vby8cff8zAwAAnT55UCpc7HI4wntX/KCoqory8XLnzXLp0iY8//pi8vDx8Ph8tLS2MjIzg8/nIzs7GaDSSk5ODwWCgt7cXURSVkPbw8DCfffYZTqeTqqoqGhoasNvt7N27l7Nnz7Jo0SLsdjs7d+5k9erVlJWV8Zvf/IannnoqRNiDg4OcOnXqK2ME4UAURdrb29mxYwf//Oc/mT9/PjNnziQSPcbjEnl0u910dHRw/vx5pk2bhiAIDAwMfOv9WiwWRkdHqa+vp7i4mKysLPx+P0NDQ1y4cIGGhgbKy8vxer309vaG4UzGkpmZqfzb7XazZ88eRFFkxYoV7Nu3D0DpAhAUv1arRavVEggEFBEEuwg0NzezZs0aFi5cyOzZs/F4PLS1tXHvvfeybNkyhoeHcbvdVFdX4/f7SUtLG9P5OGjyjdc5X41Op6OtrY3U1NQJv3N8U8IubJ1Ox4IFC3j44Ye59dZb2bVrF+np6axbt+5bRRHtdjuvvfYat956K3fddReLFi1SFi3cdttt2Gw2tm7dypEjRxSRjAc6nU4RbDCn5eTJkzQ0NNDR0cHw8DCBQIDLly/j9XoBlJyY1NRU5QE6mJeu0+mYMmUKOp0Oq9WKKIp0dHRQXV2NRqPB5XJRUFBARkYG+/fvZ9q0aWO+x/T0dO6+++6QnOvxwOv1snfvXhoaGqiurubWW29FkiT+9Kc/jetxb4SwC3vq1KlIkkRpaSkFBQVUVVVx8eJFmpubmTdv3g15RoJ3gEWLFrFhwwZyc3MxGAz09fUxffp0iouLmTFjBmVlZVy8eJH29nYyMjKUes/jRWpqKs888wwDAwP4/X5qampoaWnhwQcf5KOPPuLgwYMUFBRw6NAhkpOTKSgoUC4KQRAQBAGHw0F7eztOpxNZlhkdHUWWZfLz8+nv72d4eJjCwkIMBgOtra0UFxcTFxcXMg6NRjPuqQeSJDE4OIjFYuHHP/4xRUVF2Gw22tvbqaysHNdj3whhD6n7fD4CgUBI0o3H40GW5RtehiRJEl6vd0x2miiK+Hw+pVVbkNHRUfR6/YRmsvl8PrZv305TUxNPPvkkDQ0NvPrqq3R0dJCens6GDRtYsmSJYl/Lskx3dzdvvPEGx48fJycnhx/96Ec0NjZy5swZnn32WZqbm9m6dSuVlZXMnz+fl19+mWnTpnHvvffelNRTv9+PKIohbacDgQAulwubzTbh4/kq1FyRMCJJktLeIuhPD9aavtoHDyh9FIM2efDvrtxHsFCkIAiIohhiu6tcG1XYKjGJeumrxCSqsFViElXYKjGJKmyVmEQVtkpMogpbJSZRha0Sk6jCVolJVGGrxCSqsFVikv8Dt1bui4B+m6EAAAAASUVORK5CYII=)
Physics-General
Physics-
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
Physics-General
Physics-
When the rectangular metal tank is filled to the top with an unknown liquid, as observer with eyes level with the top of the tank can just see the corner E; a ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid will be
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)
When the rectangular metal tank is filled to the top with an unknown liquid, as observer with eyes level with the top of the tank can just see the corner E; a ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid will be
![](data:image/png;base64,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)
Physics-General
Physics-
Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is 30°, what are the angles of reflection of the light ray at points Q, R, S and T respectively
![](data:image/png;base64,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)
Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is 30°, what are the angles of reflection of the light ray at points Q, R, S and T respectively
![](data:image/png;base64,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)
Physics-General
Physics-
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 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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)
Physics-General
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
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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,iVBORw0KGgoAAAANSUhEUgAAAK0AAACACAYAAAB5nemrAAAgAElEQVR4nO1de1BbV37+7tWVhJCEeIiXeAhsDAZsYwzGi992YtfZxFkncduk7mbTdbrZtm432e7sJDvbdrad2elOtzOZTNudtpvtJml2ujvNOJPdOm78wDY2Boxt8AMwCBAgIYQeSAhJV4971T/oPcs1SIAtHsJ8MxrQ1bn3nCt995zf+T2pSCQSwRrWkECgl3sAa1jDQrFG2jUkHNZIu4aEA7PcA1huRCKRGa/pnz0MiqJE/z/8WsPi44kibSQSQSgUQjAYRDgcRjAYhNvthtPpJK9AIIBgMCh68TwPhmEgk8lEL6VSifT0dKSnpyMjIwNKpRIMw0AqlUImk4Fhnqivd8lArXbtQTAYhN/vh8/nw+TkJEZGRjAyMgKbzQaPx4NwOBy3vpKSkqDRaJCTkwOdTofs7GwkJydDoVBAoVBAIpHEra8nGauStBzHYWJiAuPj47BYLBgdHYXVaoXdbhct+RRFQSqVIikpCUlJSZDL5ZBKpaBpGhKJhPylKAo8z4PjOPKX4zgEg0EEAgGwLAuWZcFxnGgccrkcWVlZyM7Ohk6nQ2ZmJtLT05GcnLzUX8mqwqoird/vh9VqhcVigdlsxsjICNxuN3ieBzBFUrVajdTUVGg0GqhUKiiVSvJXqVRCLpdDIpGAYRjyoigKHMchHA6Tv+FwGH6/H16vF16vF5OTk/B6vfB4PHC5XHC5XGBZloxNJpMhMzMTOp0O+fn5yM7ORkZGxpoI8QhYFaT1+Xzo6+uDwWCAzWYjsikASKVSZGZmgud5WK1WKJVKaDQapKWloaamBkVFRaJrhUIhdHV1wWw2k2MMw6C+vh4qlWrW/q1WK7q7u+FyueD1euF2u0HTNEpKSmC322G1WkUPj0qlQmZmJnJyclBaWgqdTgeZTLZI387qQ0KT1uv1wmAw4N69e7Db7XC5XOSz1NRUFBcXY926dUhPTwfP8/B4PORzmqaRnZ2N1NRU0TU5jiMkEyCRSKDX6yGXy2cdh8fjwdjYGILBIICpGV2hUCAnJweTk5NElh4YGMDAwACRoxmGQUZGBgoKClBZWYm8vDxIpdK4fT+rFQlJWr/fj97eXnR0dJANFTA1qxYWFqK0tBT5+flISUlBcnIyaHr51dHBYBA+nw8ulwsGgwG9vb0YGxsDMDVutVqNoqIibNu2Dbm5uStizCsVCUdaq9WKS5cuwWg0IhAIkI3V+vXrUVtbC71eD6lUumJlRUHtxrIs7t+/j9u3b8NmswGYmnnlcjm2b9+Offv2LfNIVy4ShrSBQAA3btxAa2uraJlft24ddu7ciXXr1iWkct/r9eLOnTtoa2uD0+kkxzMzM3H48GGUlJQs4+hWJlY8acPhMCwWCxoaGjAwMABgakbKycnBzp074fF4cPXqVTLjSiQS1NbWYvfu3aLrNDU14fr16+Q9wzA4cOAAtmzZErP//v5+XLp0CePj4+SYTqfDK6+8EnPMly5dQkdHBzkmk8nw4osvIi8vb9ZzHjx4gMbGRjgcDrKCSKVSVFdXY8eOHUhNTV0TGf4fK5q0wix0+fJlBAIBSCQSaDQalJeXY/v27dBoNMs9xLjDaDTi2rVrGBkZgc/nA03T0Ol02LNnD4qKita0DFihpOU4Dg6HA62trbh9+zZ4nodCoUBxcTFqamqg1+tXtXUpGAyio6MD7e3tGBsbQzgcRkZGBnbs2IHy8nIolcqEFIXihRVHWpZl0d/fj7a2NgwNDYHjOGi1WlRVVWHLli1ISUlZ7iEuGUZGRtDW1obe3l5MTk5CqVSioqIC27ZtQ3Z29hNL3BW1xfb7/bh37x5aWlrgdDoRiURQXFwMrVYLlmVx8+ZNAFNy68aNG5GVlSU6PxAIwGAwEFUSMCW71tXVRdWxAlPkMBgMxAxLURR0Oh1KS0tnbR8KhdDb2wur1Srqp6amJqaJ1mKxwGAwED0tRVHIzs5GeXn5rO29Xi8AEFnW6/Xi1q1bGB8fx969e1FQUBC1r9WMFUNav9+P9vZ2tLa2wuVyQS6Xo7KyErW1tYhEIiKC0DQ9q2xH0zSUSqXIYCD4EMSCXC5HamqqiLQKhSJqe4qiZu1nLpFF6Gc6aZVKZdT2ycnJKCgoQEFBAfx+P3p6emAymWAwGMCyLA4ePIji4uKYfa5GrAjxIBAIoKWlBTdu3CDLYF1dHaqqqlblZutREA6HMTo6isbGRvT19YHjOGRlZeHAgQPYuHHjcg9vSbHspOV5HhcvXsTNmzfBsizUajV2796NzZs3x5ztnkTwPA+Xy4ULFy6gu7sbPM8jIyMD+/fvx6ZNm5Z7eEuGZSftlStXcOXKFXAcB41Gg/3792Pz5s2rWjvwuAiFQvjNb36DO3fugKIoZGRk4NChQ1Fl8NWGZSNtJBJBW1sbzpw5A2DK/i6VSonTCQAoFAqcOnUKMpkMXq8X58+fx71798jnSUlJOHny5Aynl+lob2/HhQsXiJugRCLB5s2b8eyzz87anmVZnDt3Dnfu3CHH5HI5vva1ryEzMzNqP3fv3sX58+fh8/kATMnXFRUV+MpXvjJr+2AwiPPnz+P27duifk6cOIHc3NwZ7U0mE86fPy/yPqMoCuFwGJFIBDqdDocPH0ZhYeGq1yosC2nD4TDu3buHM2fOIBQKQaVSYc+ePairq1vqoSQ0eJ7HZ599hnv37oHjOBQXF+Ppp59GTk7OqraeLfmd8TyPnp4eXLx4EaFQCElJSdi+ffsaYR8BNE3j8OHDKCsrA8MwGBgYwNWrV4m6cLViyUlrtVrR3NyMyclJYlvfuXPnUg9j1UChUGDfvn0oKiqCRCJBT08P7ty5Q5zgVyOWVE87MTGBmzdvwmq1IhKJoLKyEnv27AHDMGBZFkajUeTpJCjso23KxsbGYDQaRXrPzMzMmJ5RwWAQAwMDcDgcon6qq6ujOmDb7XYYjUaRk3d6ejrKysqi9hMKhWA0GonbodBPVVVVVEOHw+EgLpdCP6mpqVGND0NDQzCZTOB5nsS2hUIhtLe3IysrCxUVFatSTFiyO2JZFnfv3kV3dzeCwSD0ej127dolUmstNI/Ao+YdeJTz4tVXPPsRPpdIJCgoKMC2bdug0Wjg8XjQ2NiIkZGReY0x0bAkGzGO49Db24tz587B6XRCq9XiyJEjCesDu1Lh8/lw/fp1tLW1gWVZFBcX4/jx46su+ndJZlqPx4P29naMj49DLpejrq7uiVDNLDWSk5NRU1ODwsJC0DSNwcFBtLa2Lvew4o5FJ20oFEJ3dzf6+voQiURQXl6OsrKytQC+RYDZbMbnn38Oo9EInufB8zxu3LiBoaGh5R5aXLHo4sHExAR+/vOfY3x8HNnZ2fid3/kdYiiYnJwEMKW6KS0txfHjx6Nex+v14ty5czOMC6+//vqcxoXz58+LjAtbtmyJaVz44osvZhgXXnvttTmNC+fOnZthXDh27Nis7YPBIM6dOzfDuPCHf/iHUY0L586dExkX1Go1vvWtb5H3kUiEhKk3Njbi6tWr4HkepaWlePnll6OOPdGwqKTlOA6ff/45bt68CalUivr6eqItWMPigmVZvP/++7Db7UhOTsZTTz2F6urqVSGSLap4MDQ0hJs3b4KiKBQUFKCiomKNsEuEpKQkPPXUU5DJZPD5fLh586ZInZjIWDTShkIhNDY2AgCUSiU2bdqE7OzsxepuDbNg48aNqKioAACMj4+ju7t7Rr6xRMSiTXv9/f0YGBgggXkFBQXo7e2Fx+NBUVER0tLSZixVfr8fJpNJFCLOMMycEbOjo6MinSRN08jLy4sqg7IsC5PJhImJiQX1Y7VaRTIlTdPIzc2N+TD6fD6YTCYiv8/Vl8PhgMlkEjmkZ2RkoLCwcNb24XAYZrNZZCyRSCQoKytDUlIS6uvr0dfXB4/Hg76+PpSWlsaUzRMBi0LaQCBAVC1CBIJCoYDZbMbExARCodCs53EcB6/XKyLTfLQMgUBAdA5N0zF/mHj2k5GREfOchfYVDAYxMTEhIm0sPWskEoHf75/xAAobsoyMDFRWVqK5uRlWqxX9/f1IT09PaNfPRdmIdXd349NPP0UgEFi1Cu5EQSQSgdlsxn//93/D7XajrKwMhw4dmvNhW8mIu0wbCoVw+/ZthEIhUBSFrVu3rhF2GSGIF4KD+ODgIPFXSFTEnbRClm2e56HT6Z64+KWViKSkJJSXl0Oj0YBlWQwNDRF9ciIi7jKt0WgkX0hycjLee+895Obm4vjx48S7qaurC5cuXSIh0hRFoaSkJKqXPzC1oWloaEBXVxc5JpfL8eqrr0YNfuzp6UFDQwPZ2FEUhaKiIrz00ktR+2FZFg0NDbh//z45JpPJ8Ad/8AfQarWznmMwGHDp0iWSapSiKOTn5+P3f//3o/Zz6dIltLW1kfdSqRTPPvvsrB5qdrsdDQ0NGBwcJMeSkpJw6tQpUTuTyYSGhgZR5HJKSgq+8Y1vID09Hfn5+XC73RgaGoLH44mab3elI64yrcfjwaeffor+/n5QFIXvfve7SEpKitfl1/AY4HkebW1t+PzzzwEAR48eRVVVVUJuyOI605rNZjLbVFZWrhF2BUFIIp2Tk4PR0VEYDAaUlZXFzLswHS6XS5RoWigDsBz+unEjLcdxRKVF0zQKCwsxPDxMPqcoCikpKU9UWqOVhoyMDOTm5sJqtWJwcJDkmJgP/u7v/g5nz54lfh4vvfQSTp48uSx5KeJGWrfbLUqWxjAMmpubyec0TaO8vJxYaASMjY3BbreT90JKomhfhlAMZPpGQlCmx4LNZhNFEVAUhZycHKSlpc3aPhwOo7OzEw8ePAAAFBQUoLa2dk4ztN1uF6VloigKWVlZUVVMgUAAVqtVZHyIdT9utxtWq1VUSkqtVs9IkeR0OmG1WkFRFDZs2ACJRAKVSgWdTofu7m74fD4MDg4iMzNzXrNla2srfvKTn2Dv3r1ztl1sxI2005cPvV6PyspKVFdXz+u86a5zQjrPaKQNBoOwWq2ifLEymWxO0gobkOn9qFSqWUnr8/nQ2NiIzz77DMFgEEqlEkNDQ/inf/on6HS6BfVD0zQUCkVU0oZCoRkPrlQqjXo/Pp8PZrNZFJKTlZU1g7STk5MYHh4GRVFYt24dkV21Wi00Gg38fj+GhoZQU1MT836Ee+rp6cH69evnbLsUiCtpBXk2Pz9/3gJ+aWnpgpJMaDQa7NixY8HjKykpmVdWbZ7n0d7ejv/4j//Ac889hxdeeAFKpRKffPLJvJx91q9fv6AfV6VSoba2dt7tc3NzZ3VdfBiFhYWzmn7T09OhVqsxOjqK4eFh8Dw/52/V0dEBr9eL9957DwBQW1uLo0ePLtueJS6kZVmWZLBOTk5GZmZmQu5KgamZ7OrVq8jLyyOEBRBTTZZIEEqjMgxDqvJEy04u4N69ezh48CDxlygoKFjW3zcupPV6vcRhQ6vVzlu4X4nw+Xzo6urCM888k9D38TA8Hg9u3LiB4eFhyGQyyOVyeL1eDAwMzEnaa9euYf/+/Thx4sQSjTY24k5aAPjVr35FnGIoikJhYSGOHj0KYMr4cPXqVVHNr5ycnJhRCxzHobGxURS1IJVK8fzzz8dcKg0GA65evUo2OQ+PZTYEAgFYLJY5f8jpEJJkTFcJCTN1NFy9ehXt7e2i+zl06BDWrVs3o63D4cDVq1dF2hghakOA3W7H1atXYTKZZm2TnJyM7du3o6qqCk6nE+Pj4/B6vTAajTPqUzyMO3fu4I033ojZZikRF+NCT08PTp8+DZZlceTIEWzZskUk/1EURd4LtWVFg5j2eTQIdWmnQygBGg2P0tfw8DBOnDiBt99+G1/+8pdjjulx+pntfqLl0o1EIuA4bkbWmOneYvNpI8Dr9eKXv/wlhoeHoVar8e1vfzvqOE0mE9atWweGYUDTNLKysvD9738fX//616Oes9h47JmW53n4fD6wLAuapqHRaGKm6KRp+pEU0vNJWhyPvpKTk6HT6fDxxx+TzDfvvPMO3nrrragbxkfpZyH3M5+Hej5tBCiVSiQlJYGiKHg8HrAsG3VTlZ+fL0oKuBLw2OaMUChEfDnVanXMNPGJgIyMDPzt3/4tfD4fdu3ahV27duHpp59elozb4XAYVquV+Gg8KmabgVNTU8lDM13dlgh47Jk2HA4T0gpVvBMdpaWlOH369HIPA83NzThz5gx27tyJ5557bsHnu1wuOJ1OmM1mkm9CgEajgUQiQTgchsPhQH5+fjyHvqh4bNJOn2lVKhX8fj/u378v2oip1WqywZiYmBApx4GpJTmWrpbneYyMjIhmBJqmsX79+pg7fJfLhZGREVEOLpVKFXcludvtxsjIiEjhr1QqY+qFR0ZGRJYzmqah1+uJUaWlpQVnzpyBVquFyWQiITMChDy70WAymdDW1obu7m5cvHgRJSUlItI+0TOtEE4CTJEvEolgfHw8qhwUDAbhcrng9/vJsWjhN9Ph9XpF0aSCf0MsBINBjI+Pix6QxYiYn+2epptZZ8Ns9yNoQm7duoUzZ84gLy8PwWCQWM2mX/9hedjr9aK/vx8ulwvBYBDDw8OYmJiAw+GAQqFAfX09CTQFph40YfM4PVQnERCXjZhAOqlUCp1OF3OG0Wq1Uf1So4GmaZSVlc1pqn0YWVlZM8o2LQYyMzMXHCy4YcMGbNiwgbzneR5WqxXXrl1DS0sL8QmQyWSQSCSYnJxESUkJ8vLyIJPJYLFY0NPTQ1YoiqIgk8kQDAZx9+5dAFOTwYMHD/Dmm2+iqKhIpJbkOI5sHhMtLehjk1aoqg2AqEXWMDcikQgmJiZw9+5d4sgTCATgcrnAMAyZSWmaBsdxMBgMsNlsSElJQTAYhM/nQyQSQVdXFyYnJ3HixAlotVoMDg6SFe+zzz7Dq6++ioMHDwKASAfsdDrR0dEBv9//5JGW53myFK6Rdn5obW1Fe3s7FAoFWJZFIBAQpfZ8WLcqfKdut5ss6xRFgaZp2Gw2jI6OwuVywePxkNy5Ho8HycnJ+N3f/d1ZxyCVSomO+4kk7WqdaQ0GA9577z20tbXh9ddfx1e/+tXHTpz33e9+FyaTCTU1NaAoCpFIRDSrJicng2EYSKVS8DwPiqIQCoWILC6TyaBWq0HTNEkyl5ycjNHRUeTl5SEvLw9yuRxnz56FWq3Gv/7rv5K+JRIJdu3ahdra2oQmLQVg9SbnX4GQy+V4++23sW3bNvzlX/4lcnNzYTAYYLVaUVBQgB/84AcoKipa8HXD4TB4nieVLAcGBvCd73xHJMeuZDQ0NGDfvn3zyjXGPO5u2mw242c/+xl4nsehQ4dQX1+/KpKcAcD777+Pd955B06nE8XFxWhra3tsT/13330Xb7/9Nk6dOoXNmzdDp9NBr9fj17/+NSYmJuDz+eBwOJCSkjJjVud5HpFIhKxmgv+C0WiEx+MhM/PmzZtx/PhxPPPMM9BoNPjRj340QzXIcRx+8pOfwOFwzGnKXWl47LV8ugwWDodXRa4oAU899RRef/11PPPMM/irv/qruORvePPNN3Hs2DFcuHAB9fX1qKyshMvlQk1NDd544w14PB78+Z//ORobGzE+Po7R0VEMDg5iYGAAN2/exPXr19HX14f79+/jH/7hH1BfX49f/vKXaG9vR2dnJ86ePYva2lp88skn2LVrFzo6OvCjH/1oxoz7sMiRSHhsmZamaUilUgQCAbJEuVwujI2NIRKJYP369QmbKbGoqAg//OEP437djz76CB999BEaGhowMTGBvr4+2Gw2tLe3o7KyEllZWfjoo49w584deDweZGdnE923SqVCIBCAUqnEiy++iIMHDxJjic/nA03TeOGFF8CyLH72s58hNzcXFy9eRHl5OV544QWMjY3B5/NBrVYTh51Es2LGjbTAb+Uqj8cDo9EIjuOg1+tnkNbhcGB4eFhkVEhNTRXpLR9GKBTC8PCwaMagaRqbNm2K+qU7nU4MDw+LDB0pKSkx9b3hcBjDw8MzrG8VFRVRHYGEkKHpGxqVShW1Ko3ghrhhwwbcu3cP69evx9jYGFQqFViWRU9PDzo7O+HxePCd73wHzz//PG7duoXx8XFyTnFxMV588UXRdVmWhdlshtvtxo4dO1BWVgan04nMzEyUlpYiEAhgZGQETqcTer3+yZ1pp3sXCeKBUO49GnieRyAQEJlX52MVC4VCJKM3MLUbjiWTC/1MN68uRj8cxyEYDJJzKIqac/YS1ISbNm3Cpk2bSDAjTdNoa2vD3bt3IZfL8Wd/9mfw+XzgOI7ExdXV1c26eqWnp2PXrl0x+/3Sl74EYCrTpHBPiTbTPrY/rcPhwOnTp2E2m1FVVYWDBw+u+jBxp9MJk8mEjRs3LmiWEspS1dbWLvtmdXBwEJ988gk8Hg+2bNkS02F9peGxN2IMw5Cdqc/nW3G+l/GE1+vFz3/+c/z93/89FArFgv17pVIptFotTp06hQ8++GCRRjk/TE8nGqtmxUrEY4sHDMOQmXVycjLhFNXzgd/vx+nTp/Ev//IvCIVC+Od//mcUFxcvmLQSiQR6vR5vvPEGvvnNb+L999/HW2+9taizHMdxuHbtmihUiWEYaDQaQtqF+oIsNx6btFKplJB2fHwcv/jFL0RhJFlZWfijP/oj8r6vrw8XL16E0+nEa6+9JsqibbVacfHiRVHeALlcjjfffDPmGJqamkQeTBKJBAcOHIga02+323HhwgUYjcY5+/H7/fjGN76BTz/9FF6vFzRN46mnnnosy18kEsHk5CR4nsedO3fQ0NCAv/7rv4ZWq0VHRwcuXrxIVixhs/nMM8/Mei2WZXHhwoUZ8XOvvvoqtFotJBIJ6uvrZxTMPnfuHCFtouWqfWyZNhKJ4O7duzh9+jRomsbx48ej7poTGf/1X/+Fv/iLv0BOTg4uXLgArVb7SHJpJBKBzWbDyZMnYTQacerUKfze7/1e1Ew3i4WPP/4YBoMBFEXh7bffTigNQlyMCwqFAgqFAjzPw+12z+lLmoh4+eWXMTY2hm9961t46623Hrk8vcPhwI9//GMcPHgQFy5cwBtvvLHkhBXiwoApFWAiERaIUwh5UlIS1Go1/H4/SdqRqAaFuXDy5Em88sor6O3thUqlWrC6yGaz4dvf/jZycnIWaYRzw+l0EtImYsWhuDBLyFoyNjaG0dFRWCwWBAIBIttSFIW0tDSSS8DlcsFisYhm5JSUFOj1+qh9hMNhWCwWUb4EmqaxYcOGmDOF0+mExWIRydlpaWlRY6I4joPFYsH4+DgyMzNnJVdycjKqqqqi9hkLjyo6+Xw+jIyMiKIXGIYRXc/r9cJisYjaSKVSko3d7/fDYrGgq6uLRJs8inPOciMupFWpVGQHarfbYbPZ4Pf7RaSVSCSEtCzLwmazidRjPM/HJK0gekzPci2RSGZNbjEdfr8fNptN9IDE2vVP7ydWKPxSIxgMwul0ikJjZDKZiLTBYBAOh0MUSyaXywlpw+EwbDYbjEYj/H4/SU6XaIhbJvD29nZ88cUX8Pv9ePbZZ1FdXZ2w+bxWM1wuF/7nf/4HBoMBaWlp+JM/+ZOEK64dN4/t1NRU4rZnNptXlbfXaoLT6SQzcUFBQUI67cdtt6TRaJCamorR0VEYjUaEw2ESaNfS0oLe3t7fdsowOHr06JLvmp9EcByHlpYWdHd3o7i4GFKplOQcKywsXCNtdnY2+vr64Ha70d/fj02bNkEqlaKmpmZGWc2HK6u43W5cuXIFfX195JhMJsMf//EfR12+Ojs7ceXKFbITpmkapaWlOHLkSNRxejweXLlyRfQQyWQyvPbaa/Pyl+V5Hp999hl+8IMf4NSpUzh58uSc5zwK3n33XVAUBb1ej2PHjs3apqmpiVTGBKYmg4MHD4qyrUskElRXV6OyshJ+vx9NTU3EtVGv1y+7D8SjIK7VbXp7e/HFF1/AbrejrKwML7/88oLOj0QiM3SfsWaC2doLwYHx7Gc6/H4/tm/fjry8PBw5cgRvvfXWvM5bKKZvYqPdz0Lvf2BgAJ9//jlsNhuxsiViYcK4rg06nY4Uan7w4IGojsB8IESYTn8ttP18Zo6F9jMdH3zwAdlozoZAIIB3330X2dnZqKqqwi9+8Qs4HA4cO3YM3/ve91BeXg61Wo1/+7d/ww9/+ENkZGTgueeeQ2dnp+g687mfhdw/x3EYHR2FzWYj2XkSzSVRQFxJq1QqUVhYSL6M9vZ2TExMYHR0lLysVqvIqcbj8Yg+Hx0dFekZVxLMZjN+/OMf42tf+1rUNv/+7/+ODz74AFarFR9//DFomibKfIfDgevXr+Nv/uZv8L3vfQ86nQ4XLlxAYWGhqIr648Lv9xOd+fQsMkJ+W0H/nKjanbibrYqKinD79m2wLEucOKYnA5ZIJNizZw9JAdTf3y+aZWiaRl1d3YwshRzHwWazzagCrtfrY6ps3G43KXsK/LY0VDRL0PR+0tPTif6ZZVl8//vfxz/+4z9GPZdlWbz77rv48MMPAfzWwVsI5/7TP/1TpKamwuFwYP/+/Xjttddw8+ZN0DQ9Z/0CQd883TmdYZhZ9axWqxW3bt1CIBDA888/D4VCAbvdThIuFxYWQq1Wx+xvJSPupM3JyUFOTg6JE1MoFHjllVeitq+qqpqXdUmwiJnNZnJMIpFAp9PNSVqDwUCMC0IJ0GjE43keo6OjMJlMKCkpIaTt7e3FlStXUF9fjw8//BAdHR1ISUnBzZs3iTfZ8PAwLBYLyWsrwGg0oqysjPR57do1UiJUiP2aq/iHUI1mukVQJpPNStqioiKRpUtIye/xeMhquJIMJwtF3EnLMAyqq6vR398PlmXR0dGB0tLSx36y5XI5qqur51XmaTqiVXmJBqlUiq1bt2Lr1q2i4wqFAq+//joxkwry+nS5XZjNXS4XpFIpDAYDKQKYlpYGlUoFt9uNBw8eYNeuXeRB5Dhuzpxj6enpc6aZn4ggOFcAAAxMSURBVA2RSARjY2MwGAwApr6PvLy8hFR1CVgUr5bCwkLo9Xo8ePAANpsNvb292LZt22J0tWQoKSnBO++8AwAkuDI7Oxv79u0jbfLz87F3715885vfRGpqKmpqapCRkQGPx4ONGzdCoVCgpaWFmLQnJiZgt9uxYcOGRVuueZ7HvXv3SAHn9evXJ3w4VFxVXtMxMDCADz/8EBRFobi4GMeOHUtoOWo6QqEQ+vv7IZfLZzicdHV1wWg0QiaTYcOGDcjOzkZ/fz/S09ORnZ2NsbExdHd3Y+/evSTCmGGYBa0GC8HIyAj+8z//E36/H+vXr8eXv/xlpKenL0pfS4VFIy3HcfjVr36Fnp4eKJVK7Nu3DwUFBWhqahIlE1YqlfjqV7864/yenh5cv36daBIE545Dhw5F7dPn86GpqYkshcDUcv/yyy/HTL7c1dWFpqYmEqlL0zQ2bty47CU1m5qacOfOHfKeYRgcPnw4KsEtFguamppE5VSFTN9KpRK7d+9GXV1dQosGwCKSFphSEf30pz8FRVEoKCjAoUOHoNVqRW6CghP5wwiHw6IsKMDUxiuWbjESiSAYDIr8HiiKIkUxomG2vhiGWXbn6GAwOMOhXi6XR1VV8TyPYDBIvt+7d+/i7NmzAKZEl5deeinhghhnw6J6aut0OnzpS19Cc3MzzGYzurq6sH///nmVp2QYZsGO5PPJNxCvvpYCMplsQQ/OdNWZsOoAU6tZXV3dqiAsEGfjwsOgKAo7d+5EVlYWOI5Db28vjEbjoqSQX8NvIUTger1eIlbFqs+QaFj06UWhUGD79u04f/48bDYb7ty5A61WSzy8XC6XyGAgJAWOJYOyLEtqCwiQSqUxdZ1CQuLp/QhqqFjw+/1wuVyizDRyuTxmmIpQd2K6OkyoFh5tJWBZFuPj46J+Yt3TxMSESGdLURQ0Gg3UajX6+vpw9+5dcBwHjUZDssqsFiw6aRmGwYYNGzA4OIjOzk709PQgJycH27dvh0wmg8lkQnd3N2kvkUiwbdu2mKQV0r5PJ6FKpYpJWrPZLLK8SSQSVFVVzUlal8tFEsEJEDQB0cDzPIxGI/r7+8kxhmGwe/fuqKR1u924e/eu6AHWaDRR78lisZDaCsCUaFBeXg6tVouWlhZ4vV5IJBLs2LEDOp0u5j0mGhZ1IyaA53n09/fj/PnzsFqtSE1NxeHDh0nuqjXEBx6PB9euXUN7ezsCgQA2btyIr3zlK8tW4n6xsCSMoWkaBQUF2LZtG1JSUuByudDY2ChSfa3h8RAIBHD//n3cv38fgUAAeXl52Ldv36ojLLBEpAWm5MDKykpUVFRALpfDYrHg8uXLj11Cc6Hw+/1obm7GJ598gs7OzlURFsRxHAYHB3H79m1MTk4iNTUVe/fuTcjw8PlgScSD6bDZbDhz5gwGBwchkUhQUVGB7Oxs9PT0kDYSiQRPP/00kec4jkNraysePHhA2jAMg0OHDol+GJ/Phxs3bmBgYEDU7oUXXiAyMsdxcDqd8Pl80Gg00Gg0RIcbiUTQ2tqKrq4u0VgOHjxIIolnw9DQEG7cuCGSe7OysqJWMW9vb0d7ezt5T9M0tm/fHjW8fHx8HDdu3BC5L0qlUpw4cQKRSASjo6M4e/YsTCYTaJrGvn37UFdXt+x65sXCkpM2Eomgv78fv/71r+F2uyGVSlFZWYk9e/b8dlD/Xw5U8N6KRCLw+XwiP1yhfOl0/apQEX26VkHYVc9XdhYqqkcby2wIBoPw+/2iWXt6Yr6H4ff7RT7DgoEl2lLOcRx8Pp9IsyBoPyYnJ3H69GkYjUbwPI8tW7bgwIEDq0YnOxuWnLTAFAkfPHiA06dPIxgMIikpCbt27XokL6YnGTzPE1N5JBLBhg0bcOjQoQVXj0w0LAtpBXR0dOA3v/kNwuEwpFIpamtrceDAAVIfSy6Xz5ghhbplD5uCY81Ss5mDoy2doVBoVtNptJl6oeMBfms2ng6pVBrVKjdbHwDw05/+FE6nExRFobCwEIcOHYopxqwWLKvtsqqqCizL4tKlSyTSwev1wuv1wuPx4OjRo8jLyxP5DTgcDly7dg0Wi4Uck8vl+PrXvz5rHz09PWhqahKlziwtLcWBAwdmtI1EImhpaRHpPxmGwZEjR6Km4x8dHcW1a9dENRpSUlJw4sSJqPfd3t6OGzdukPcSiQQ7d+7Epk2bZm3vcrnQ1NSE4eFhkiZUSDtFURRyc3Oxb9++J4KwwDLPtMDULHLt2jWykVGpVKirq8PWrVuhUqkSMsR5scBxHMbGxnDp0iUYDAbwPA+dToe9e/cuuNh1ImPZSQtMbWRu376NlpYWjI+PQ6FQoLq6Gtu2bUN6evoacTH1HQ0NDaGpqQlDQ0OkIMv+/fsTMh/X42BFkBaYUo7fu3cPzc3NsNvtkMlkKCkpQV1dXczEdE8CfD4fOjs7cevWLYyNjYHjOJSUlGD//v1PjEgwHSuGtMAUcR88eEAcxSORCHQ6Herq6lBZWYlAIIDOzk6RJU3Q19I0DZZl0dXVhZGREZSUlKCkpETke9rZ2SnS4WZmZqKioiKm/8HY2Bg6OztFRpDU1NSYpY84jkNnZ6coDb9EIkFdXd2sUQMulwudnZ2k5BLw21pjExMTpEST2+2GRCLBxo0bsXv37mXNcbucWFFOpEJaSpVKhdbWVvT19WFkZAQNDQ2wWq3YunUrdDqdSP85PUEFwzDIzs5GcnIyMjIyZogVQg0CAUqlck4FfHJyMvR6vUj3O1ckK03TyMrKEl2bpumo5yUlJSE/P19U+0AikWB4eBhNTU0YHBwEy7JQq9Worq7Gli1bEj5k5nGwomZaATzPY3JyEi0tLWhubibVtXU6HXbs2IGSkpIV6bQdLwQCAbS2tuL27dtwu93geR5ZWVnYs2cPSkpKIJfLn2g5f0WSVkAoFML9+/fxv//7v2BZlliOhOVxNWZd7O3tRUNDA+x2O0KhEGiaRmFhIQ4cOIC8vLyEzQoTT6xo0gqw2+344osvYDAYiJFAq9Viz549KC8vF5l7H8b0GelxP4+G+Z4Xq934+Diam5vR0dFBzNUymQx1dXWor69PyERxi4WEIC0wpfLp6OhAW1sbHA4HsfMXFhaitrYWhYWFaG5uFjl6S6VSHD9+nGxYLl++jFu3bpHPGYbBs88+S1RGTU1NaGlpEX1+8OBBVFZWRh2XyWTC5cuXRZtDjUYzw9hhMBhw+fJl4uRNURSys7Px9NNP4/79++jo6CCRCIIotG/fvoSsibDYSBjSCrDb7WhqakJ/fz8mJycJefV6PbZs2YKioiKywVqJch/P8/D7/fB4POjs7ERnZydJ/iGXy6FWq1FTU7PqQmTiiYQjLTC1URkYGMD9+/dhsVjIj84wDHQ6HdatW4e8vDykp6dDo9GsCDmQZVmSDG9wcBADAwMismZkZKC4uBibN29GZmbmWkRHDCQkaQX4/X4MDg6iu7sbIyMjoiQVarUa+fn50Ov10Gq1SE1NRUpKyqIVxbDb7RgaGhI526hUKqSlpcHlcmFkZATDw8MwmUxkdRACF4uKilBaWors7OxVrRWJFxKatAJYlsXw8DAGBgYwMjKCsbEx4q/KMAzS0tLIS6vVIj09HQzDwGKxiCJmpVLpjKwydrsdPT09Iv/XlJQUbN++XdROSHfkcDjgcDgwPj4OhmGQnp4Op9NJauECUzKvTqdDXl4eiouLkZmZmXAVZpYTq4K0AgKBAJxOJ2w2G4aHh2E0GuF0OkW5aRUKBdRqNSQSCVwuF3EmT0lJQVpaGrZt2waGYYirIMuyGB0dhdfrJW6LMpkMer2eeKNNTEzA4/HA6/XC5/OR/6c7rcvlcuTm5kKv1yM/P39FiS6JhlVFWgFCBIOQZdxsNsNsNsNqtc5QOwnpj6RSKWQyGSQSyayp7SORCPHzFV7hcBjBYBChUEiUjkhAUlISdDoddDodCgoKkJ6eDrVanbBp41cKViVpp0NwuBZCYoaGhjA8PIzR0VG43e4ZztiPA4VCQUqYFhQUIDc3l6Q2kkqla5urOGHVk/ZhCLNkJBJBKBSCy+WC3W4nL7/fj2AwiEAgQF48z4NhGCQlJUEmk0EulxP1lFarhVarRWZmJpRK5YKLlqxh4XjiSLuGxMfaerWGhMMaadeQcFgj7RoSDmukXUPCYY20a0g4rJF2DQmHNdKuIeGwRto1JBz+DxdC5ZvVg2NRAAAAAElFTkSuQmCC)
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,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)
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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)
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,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)
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,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)
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