Physics-
General
Easy
Question
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
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)
- 15 cm
- 30 cm
- 20 cm
- ¥
The correct answer is: 15 cm
When the object is placed at focus the rays are parallel. The mirror placed normal sends them back. Hence image is formed at the object itself as illustrated in figure.
Related Questions to study
Physics-
A thin rod of
length is kept along the axis of a concave mirror of
focal length such that its image is real and magnified and one end touches the rod. Its magnification will be
![](data:image/png;base64,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)
A thin rod of
length is kept along the axis of a concave mirror of
focal length such that its image is real and magnified and one end touches the rod. Its magnification will be
![](data:image/png;base64,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)
Physics-General
Physics-
A ray of light makes an angle of 10o with the horizontal above it and strikes a plane mirror which is inclined at an angle
to the horizontal. The angle q for which the reflected ray becomes vertical is
![](data:image/png;base64,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)
A ray of light makes an angle of 10o with the horizontal above it and strikes a plane mirror which is inclined at an angle
to the horizontal. The angle q for which the reflected ray becomes vertical is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARMAAACuCAYAAAAViumnAAAgAElEQVR4nO3deVjUVf/4/+cwMAzDAAMMO4KKBiIobimmqbmSe2qamt5llpb357blq91Zd6a5dFe2a2VWGmkuud4Ziqa5ZIoLkKKIIpsg+zIL2yy/P7x4/ySs1EZROI/r8rriPTPvOTPNvOa8z3md15FZrVYrgiAIf5NdYzdAEISmQQQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgQTQRBsQgSTu0h2djbLly8nKyursZsiCDfNvrEbcKd9/vnnFBYWMm/ePOmYXq/n448/pmvXrvTt2xd7+xt/W8rLy4mNjSU0NJQBAwYAsHDhQry9vZk6dSpKpfKGz1VUVMTu3buJjo4mKCiowe3Lli1j79690t9jx45lwoQJODk5ERsby/r167FYLABERUUxd+5cXF1db/j5BeHvaHY9kxYtWvDpp5/WO5aamsq5c+dQKpXI5fKbOl9NTQ1nzpwhJydHOvb4448zfPhwFAqFTdpcZ+PGjYwYMYIlS5YwePBg1qxZw5EjRwBYv349DzzwAEuWLOHZZ5/l4MGDrF692qbPLwh/ptkFk4EDB+Li4sKePXukY7/++iuenp60atUKmUwGgIeHBx4eHkRERPDdd99J9509ezYrVqwgKCgIrVbLlClT+PLLL5k1axZ9+/bl8OHDfPjhh2zZsoXa2lpqa2ulcw0ZMoTffvuNkpISxo0bJx3fvHnzDbX90qVLxMTE0KFDByIjI9FqtdJtqampDB8+XLotODjYRu+YINyYZhdM7O3tmTp1KuvXr8dqtXLlyhVOnTpF+/btCQgIwGKxEBUVxYIFCygpKWHlypVs2bKFxMREAAwGA3PmzOHUqVMUFRWxZs0annzyST7++GP279/PAw88gNFopLq6GrPZTHh4OO+88w4lJSX861//Ij4+nqVLlzJ58mRKSkpYvXo1Y8eO5a/Kyhw4cACZTIanpyfZ2dls374dtVpNmzZtSEpKwmAw4OfnR1lZGT/++CMZGRn06tXrTrylggA0wzETgOHDhzNhwgQuXbpESUkJXl5eREZGApCYmMjFixcZOHAgqampVFVV4eLiQlJSElFRUQAsWLAAtVr9l8+TkJBAbm4uTz75JAAxMTHExMRQVVVFfn4+qamp0nmys7P/9FyHDx/GarXSqVMnSktLGTduHCtXrsTe3p6ff/4ZlUpFdHQ0BoMBLy8vjh49avPLLEH4M80ymLRs2ZL777+fH374ARcXF+RyOW3atKl3n1mzZkn/7enpiZ+f3y0917WXIgDV1dXs3LmTNWvWoNPpqKmpuaHzJCcns2jRIiZOnMiqVavYt28fmZmZhISEkJ6ezvTp03nxxRf55ZdfmDlzJsnJyXTt2vWW2iwIt6LZXeYAODo6MmjQIGJjY0lMTKRdu3a4u7sDVwOHq6srH3zwAfHx8cTHx/Pdd98xaNCg657Lzs4OhUJBVVVVg9u8vLzIzc0lNTUVuNr72LdvH9999x0jR44kLi6OpUuX/mV7DQYD+/fv57777sPJyYmOHTsik8nIzMykqqqK48ePExgYiEwmIzIyksDAQJKSkv7GOyQIN69Z9kzkcjldunRBr9eTmZnJzJkzpduCg4OZN28eL730Ej179gTAz8+PQYMG0aJFiwbnUiqVBAcHs3XrVtRqtTQ9DNC6dWuefvpp5syZQ7du3aipqeG+++6jXbt2JCQkcPny5esGod9LSUmhoKBAuhTz8fHB3d2dnJwcMjMzycnJISwsTApsUVFRnD179u++TYJwU+Tz58+f39iNaAxKpZLQ0FC6d+9Ox44d6+WWdOvWDZ1Oh0qlQqVS4enpSXBwMC4uLri5uREeHo6vry92dnbY29vj7e2NQqHAy8uL4OBgfH19pfv06tWL6upqVCoV7dq1Y/DgwbRp0wa5XI5cLqdbt25ER0fTvXt3nJ2d8ff3p127dqhUKqk9JpOJ0NBQaUBVqVTi6+tLSEgIHh4eBAYG0r17dxwdHbGzs8PX15fg4GAxoyPcUTJRnV4QBFtolmMmgiDYnggmgiDYhAgmgiDYhAgmgiDYhAgmd4Ber2/sJgjCbSeCyW1mtVo5ceJEYzdDEG47EUxuM6vVWq88gSA0VSKYCIJgEyKYCIJgEyKYCIJgEyKYCIJgEyKYCIJgEyKYCIJgEyKYCIJgEyKYCIJgEyKYCIJgE82ybKPQUHp6OhaLheDgYBwcHBq7OcI9SPRMBEpLS4mNjeXUqVOYzebGbo5wjxLBRCA5ORmTyUR4eLjYa0e4ZeIyRyA6OpquXbuiVCqxsxO/L8KtEcGkGbNYLFgsFhQKheiRCH+b+Blqpqqrq1m7di3PP/88FRUVjd0coQkQweQOqK2tbewm1GOxWPjtt9/YvXs3o0aNwtXVtbGbJDQBIpjcZtXV1XfdVp0Wi4W8vDx69OhB7969G7s5QhMhNuG6zeLi4njuuefYunWrtL3n3cBsNlNZWYlarW7spghNhOiZ3EZVVVUsWbKE3NxcVq5c2djNAWDXrl2kp6cjl8tFIBFsSgST22jHjh0kJydTXV3Nvn37OHLkSKO2Jy0tjXfeeUdkuAq3hQgmt4nRaOTzzz/n1VdfxdPTk9GjR7Np06ZGa09lZSXvvPMOQ4cOxd/fv9HaITRdYszkNtm8eTN6vZ5HHnmEyMhIjhw5Qnx8PEFBQfTp0+eOt0ev17NlyxYeeeQRnJ2d7/jzC02fCCa3ycmTJ4mIiEAmk9GuXTsuXLhAWVkZRqPxjvcMrFYrMpnsjj6n0PyIDNjbpHPnzsDVadgXXngBAI1Gg0ajuaPtyM3NJTs7m7CwMNzc3O7ocwvNiwgmd0BjfYkNBgNbt27lypUrtGjRQgQT4bYSA7BNWFJSEunp6QwZMgQfH5/Gbo7QxIlg0oS5ubkxfPhwoqKikMvljd0coYkTlzlNkMViwWQy0b59+8ZuitCMiJ5JE2MymTh48CCrV69u7KYIzYwIJk1MQUEBK1euJCAgoLGbIjQzIpg0MW+99Rbh4eEMHDiwsZsiNDNizKSJeeONN5DL5WL9jXDHiWByF6iurubKlSvY2dnh6up6S/kgpaWluLi43PGkOEGoIy5zGlleXh6bN29m8uTJTJ48mffee4+qqqqbOkdRURFvvPEGV65cuU2tFIS/JoJJI7py5Qpr1qwhMzOTgwcPsmrVKsxmM5mZmTd8DoPBwFdffYVKpcLX1/c2tlYQ/py4zGlEK1aswM/PjxkzZgCgUChwcXHBaDTe8DmKioqoqKhg4sSJIjFNaFQimDSSS5cusXnzZsLDw0lNTQWgvLwcq9XKo48+esPncXd3Z9q0aQQEBIiVwUKjEsGkkezevZv+/fvTvXt3FAoFNTU17NmzB41Gc0MlCkpKSqioqMDX15eWLVvegRYLwp8TYyaN5PDhw0RHRzN27FjGjBlD//79KSsrY+DAgX+5IZbJZOKHH34gNjYWvV5/h1p891q7di1ff/01FosFg8HAK6+8Qo8ePaR/a9eupbq6urGb2eSJYNIISktLKSoqQqFQSJcm8fHx+Pn50b9//798fHJyMj///DOdOnXCw8Pjdjf3rhcXF4fBYACuFvE+cuQIc+fO5fvvv+fRRx/lk08+4cyZM43cyqZPXOY0And3d5ydnSkoKMBkMrFx40Y+++wzDhw48JePra6uJi0tjeDgYAYMGCD2BgYyMjJ46qmnkMlkmEwmioqK6NmzJz4+PrRu3Rp/f3/s7cVH/XYTn8RGMmfOHNauXUtoaChnzpy5oUBisVhwdHRk/PjxvPbaazg6Ot6Blt7dTp8+jaurK61bt0Ymk3Hw4EFkMhnV1dUcP36c7du3ExYWJtYq3QEiXDeSbt268fPPP9/UY1JTU3Fzc2sW1eWtVismk4mqqiqsVusfbmF6/vx5vLy8pHGmkydPUllZybhx48jJyWH69OnMmzdPLC+4A0TP5B5RWFjIe++9x7Fjxxq7KbeN1WqltraWsrIysrOzSUtLIyUl5U+T+DIzMwkJCUGpVAKQnp7OokWL2Lt3LzNmzCA7O1tkBt8hIpjcQWazGZPJdEuPXb58OSqVipiYGBu3qvGZzWZKS0tJT0/nzJkzpKamkpeXR21tLf7+/rRp0+a6j6uqqiI5ORlPT08UCgXl5eUcP36ckJAQ1Go1HTp0wGg0kpeXd4dfUfMkLnNuM6PRSFJSEpcvX6ayshKj0Uhtba2UH/Lggw/eUBq8p6cnU6dObTLjJGazmbKyMvLz89HpdJjNZhQKBc7Ozmi1Wtzd3VGpVH+aiHf58mWysrIYP348CoWCo0ePotPpCA0NBSA4OBgHBweKioru1Mtq1sS+ObfZN998w/r16xkyZAgajUYKBoWFhZSXl3P69GkGDRrE1KlT//Q8BoPhnt88y2KxUF5eTnZ2NmVlZZhMJtRqNZ6enqhUKlxdXXFycrrhGaqysjJOnTpFZGQkWq2W7OxsEhMTGT58OHB147Fz587h5+cnBmDvAJnVarXm5uZSVlaGt7c37u7uYo2HDWVlZbF582amTZuGo6Mj9vb22NnZodfrMRgMXL58mW+++YasrCxefPFFevbsKT22rKyMNWvWMGXKlHu6tIDRaOTSpUvk5uZitVrRaDR4e3vj4uKCk5MTSqVSTHE3AfZ10fvSpUvI5XKUSiXe3t74+vri5+eHu7t7Y7fxnhYYGIiXlxcuLi71jqvVatRqtZQLsXfvXt577z1kMhnR0dEArFu3juzs7MZo9t9WUVFBZmYmmZmZVFZW4ufnR3h4OG5ubjg6OiKXy0UAaWLs1Wo1Xbt2xcfHh8uXL5OTk0Nqaqq0+MzJyYnAwEACAgIIDAxErVaLBWU2ptFoGD16NO7u7rz55pt88MEH5ObmcvjwYWbNmtVgWrS4uJg333yT999/nw4dOhAbG0tkZOQdaWt6ejpqtRovL68GnwOj0Uh2djYXLlygqKiIVq1a0aNHD1xdXf9yiYBw75PPnz9/vqOjI56enlitVr799luUSiWDBw9GqVRSXV1NUVERFy5cIDk5mQsXLlBYWEhlZaWUVVg37CKTyUSg+R2r1crp06fp0KHDn95PJpPh7u5OcXExKSkptG/fnk6dOtGxY0fpi2i1WsnIyOCjjz4iMjKSLVu2UFlZicFgoG3btrc1l8JsNnPu3Dn27dtHeHg4SqUSk8mE0WgkIyODlJQUkpKSqKmpoX379tx///20bt0aZ2dncdncTNjD1YGqkydPsnbtWrp3786TTz6JQqEgIiICo9HI4cOHOXHiBP7+/iiVSvLz88nKyqK2thY3Nze8vLzw8vLCw8MDJycnFAqFND4g3DiNRsMjjzxCVlYW4eHhDX7NDQYDsbGxdO7cmXHjxgHQqlUrysrKMJvNt61dJpOJ5ORk3n33Xfr160d2djaZmZlYLBZKS0txdHSkZcuWdOnS5aYGUIWmxd5oNBIXF0dcXByDBg1i2LBh0odYr9ezf/9+du/eTVRUFMOGDcPZ2ZnS0lJKSko4d+4cCQkJtGrVipycHMxmM2q1Gnd3dzw9PdFoNKhUKpRKJU5OTiIL8S/U1NSQk5NDRUXFdQNxamoqq1at4tVXX2Xjxo0A7N+/ny5duty2L3BVVRUnT55k6dKlpKSkYDab2bZtG0OHDmXgwIG0b9/+np9lEmzDvrq6GplMxqRJk4iOjpYyCY1GI5s2bSIxMZEHH3yQoUOH4uTkBICvry+FhYUkJCRQW1tLVFQUGo2GsrIyKioqKC8v59y5czg6OqLRaHBzc5P+1Q08qtVq0f29htVq5dKlS6xbt45evXphsVgaBIhNmzbRpUsXUlJSgKvTy8nJyYwaNcqm+Sdmsxmj0UhJSQknT55kxYoV/PTTT8hkMry9vZk5cyYjR478wxR3oXmyd3d3Z+TIkchksnpf7qKiIs6ePcuUKVOIjIyUehU1NTUcPnyY2NhY2rVrx7hx4wgODgaufiGuXLlCbGwsNTU19O/fn+rqasrLy8nPz6e2tlYKJK6urlIldjc3N1xdXZv1eMuxY8fYsmULZrOZgQMHXrdnEhcXx+rVq6Xxlw0bNuDl5UXbtm3/dmC2WCxSAMnNzQWu/v90cHBgwIABtGvXjuLiYrRaLeXl5aSkpBAaGipm+wSJPXDdD66HhwdPPfUUbdu2rXd8//79rF27liFDhjBixAhUKpV0W10gycrKYsKECXTp0oXa2lppkDAxMZGEhASCg4MpLCzEYrFIl0AqlQpPT088PDzw8PBArVY3q2tvNzc3jEYjaWlprFixgsmTJ9d77wsKCsjNzcXT0xO4WtU+OTmZbt264efnd0vPabVaqayspLCwkLy8PGpqalAoFDg5OeHl5YVKpcLZ2ZkhQ4ZQXl6OwWDAaDSi1+vx8PBoMtm4gm3cdAZsfn4+OTk5tG/fXrokArh48SKffPIJcrmcyZMnEx4eLvVmTCYT+/btY926dYwYMYKePXtiZ2dHeXm59EHOzc2VBm/rCitrtVppcPdevS63WCysW7eOSZMm/eF99Ho9KpWK3NxcLl26xJ49e6iqquKZZ56hdevWwNWxixYtWrB//368vLz48ssvcXJy4h//+MdN77NTXV1Nfn4+ly9fpqKiQprqdXd3R6lUolQqxfiWcNNuerrFx8cHLy+vBr2GoqIiWrduzejRo/Hz85Nut1qtfP/996xZs4ZnnnmGwYMHS79odb2QTz75BLPZzGuvvUZFRQVXrlwhLy+PnJwc5HI59vb2aDQafH198fX1xcvLSxq/udfpdDqmTZvG1KlTGTp0KP7+/oSFhbFixQpWrFjB888/L82ivfjiiwwYMICWLVvy7LPPMnr0aNRq9Q09T21tLYWFhaSkpKDT6VCr1QQFBdG+fXtp5k2MYQl/h03X5lit1gbjHl999RXLly/ns88+o3PnzvVuS0tLY9KkSfTs2ZP58+dLKeNWq5WKigq2bdvGqVOn6NChg7QxlUwmw97eHk9PTwICAvD398fHx+eu/SX9q57JsmXLOHToEN9//329966iooLXX3+dFi1a8Mwzz+Ds7IzVar2pnB6z2UxhYSGnT5+moKAAJycnQkNDCQkJqVcyUhDmzJmDu7s7s2bNapCtfaNsmghyvQ/nE088wZAhQxpc1ycmJvKf//yHiRMnMnv2bOl4Xe7Ct99+y4EDB3j55Zfp3LkzNTU15OfnSxmWOTk5lJSUkJSUhFwuR6vVSj0XrVaLXC6X/t2tX5qCggLi4uLYtGlTgza6uroyceJE3n//fUpLS3F2dv7TAFJXTKi2tha9Xs+FCxfIz89HqVTi7u5OUFAQQUFB0qWpxWJBp9Oh0+mk51Or1VitVgwGA1arFZVKJXKFrmPGjBkEBQXxyiuvAFBZWcnHH39MZmYmixcvvulZrqCgIBYvXszkyZNt2s79+/ezYcMGnnjiCbp16/an9732h+pW3ZFPyvUGCC9fvsyMGTPqFVC2Wq3k5OTw2WefUVpaymuvvUZERAR2dnYolUp8fHw4d+4chw4dIiIigp49e6LT6SgsLESv15OYmIjRaKyXSFe3oMzR0RGFQoGDg8NdM7Dr7e3Np59++ocfvm7duuHo6MjRo0evuy+OxWKhuroao9GITqejpKSE/Px85HI5Pj4+9O3bF6PRyI4dO1i6dCmrVq3ioYceAiA3N5elS5dy5MgRqqqqGD16NLNnz6asrIy4uDgpafHahYfCjTt//jxlZWVYrVaUSiUdO3YErv6AVFZWotPpMBgMdO7cmR07dtCiRQvy8/PJyMiQztGyZUtpSCEpKUnqnXt4eEiD85mZmSgUCqn+i0KhoFOnTuh0OjIyMsjPz+f06dO4ubnRunVrzGYziYmJADg7O9OqVSubjUc22s/O0KFDGxyzWq1kZmbi7OzMM888Q1BQkHRbeXk5P/zwA/Hx8fTp04eJEyfWyxA9efIkmzdvRqvV4u/vT2VlJenp6aSkpODg4IBGo5Fmi9RqNU5OTjg5OeHo6HjHg0t5eTklJSX4+flJA6x/pGvXrqSlpUl/183A6PV6ysvLKS8vp6ysjF9++YWIiAj69euHi4uL1KM4ePCgtMy/jtls5tixY5SVlbFv3z4yMjJ49dVXOXHiBElJSYwZM4aAgADee+89EUxuwcmTJ3nzzTelv3Nzc/nwww+5//772bx5M7t27UKtVlNZWcmqVat49NFHWbJkCSqVii+++IKSkhJSU1NZvHgxEydO5MCBA8ybNw8/Pz8MBgNqtZqFCxcSFhbGsmXLKC8vp7KyErPZTEpKClu2bAGu7niQmJhIaWkpBQUFzJw5k3Xr1hEfH09NTQ21tbU89dRTjBkzxiav+67qw9rZ2dG1a1c6dOjQYIbi0KFD7N69mylTptCrVy8pkJhMJk6ePMm6deuQy+WMHDmS4OBgKXnu0qVLHDhwADc3N3Q6HWfPnkWhUNRLpHNxccHFxQW1Wo1Sqbytl0U1NTXExcVRWFjIhAkT6s2IXY/ZbCY0NBS9Xo9er5cSA+u6pW5uboSEhHD27FnWr1/PAw88UO/SZMSIEcDVsatrz5mTk0N0dDSurq60adMGFxcX8vPz0Wq1nDlzhtzc3GZRa/ZW/frrr7z//vvA1cHtQ4cO0aJFC8rLy1m0aBG9e/fm2Wefxd7ennfffZcFCxawYcMG4OqM6Ny5c+nRo4d0PgcHB4YMGUL//v3ZtGkTP/74Ix06dKCsrIznnnuON954g7Fjx1JQUMDixYv58ssvWbhwIXC1d7J+/Xq8vb2ZPXs2sbGxLFy4kOnTp+Pm5lbvMictLY1Nmzah0+n46KOP+PHHHxk2bJhN3pO7KpgAUo/h9/z8/Hj55ZcJCwurd/zAgQPExcURFhbGo48+KiVRaTQa9Ho9J06cQKfT0adPH1q2bEllZSXl5eWUlpaSlpaGwWDA3d1dGjOoS6TTaDS4urr+5Zf9Zp0+fZpffvmFQYMG/eW1tdFolFZrJycnS5dpGo0GrVaLi4sLDg4OyGQyHn/8ceLi4ti/fz/jx4//0/PWDXDXvVd1Sx4ABg0axPnz57Gzs+PBBx+0zYtugiwWi1SC02w2Y7FYgKuzmgaDgYEDB0qzlgMHDmTjxo0UFhYC0L17d1q0aHHd8168eJH9+/fTu3dvwsLCOH/+PCaTibFjxwJXK+516tSJ+Ph4ysvLAYiJiZEuVSIjI/+0UPnjjz/O//t//w+z2cyZM2fw9vamsrLSBu/IXRhM/sjvZ4LqyGQyhg0bRufOnaVpUovFwoULF/jmm2+wWq089thjRERESL2Z6upq9uzZw6+//srDDz9McHAwJSUllJSUkJGRgaOjo5RI5+bmhoeHB+7u7ri7u//tpfQ1NTX07t2b6OjoBueyWq1UVVVRVlZGYWEhZWVl+Pv74+TkhK+vr5Q9fL2ZK41Gw5gxYzh06NBfBpPfMxgMVFZWSluTBgYG/q3X2Bz07NmTl156Cbg6ACuXy6XC17W1tVJwsVqt1NTUNMgwv56Kigq2b9+Ovb09I0eOlH5Ur92N0GKxUFtbK00u/J7FYvnDXR7T09P5v//7P8aNGyf92NoqkMA9FEz+SN1evdd27WtqakhPT8fLy4uRI0cSGBhY743fuHEjW7ZsYdy4cTz00EOoVCpqamqorq4mOzubb7/9Fq1WS2BgILm5udjb2+Po6CjNjNQN7mq12pu+JOrQoQMRERH1Br1qa2spKSkhJyeH4uJinJycpEE2Z2dnlErlDQWx6OhoPvvss7+8n1wux9vbm/j4eCZNmkR6ejoODg74+PjcNYPT96qAgAB8fX1Zu3atVBZi27ZtdO7cGR8fnz99bFpaGnv37uWll17C29sbgDZt2uDh4cGyZct44YUXKCgokEpV/lWyorOzs7TOCq7uT33kyBF2796NXq/n2LFjIphc69p0/jqOjo706dOH3r17NyhK/Mknn7B161beeecdwsLCpK6og4MDxcXFvPvuu4SFhfHMM8/g4OBAVVUVeXl55Ofnk5ubS2FhIRcuXEAul+Pg4ICfnx8+Pj74+vqi0Wj+8Nfi8uXLFBcXS+tqTCaTtKXD+fPn0Wg0+Pj4EBUVhaurq5REdjPBytXVVdoms87KlSt5//33SU9PZ9KkSbRt25YDBw4wZMgQDh06RGRkJCaTif/85z906tTphp9LuD6lUsmHH35ITEwMa9euRS6X069fP959990/zYUyGo3Ex8fz888/89tvv6FQKJg2bRqzZs1i586d3HfffXz44YeoVCoeffRRZsyY8ZfT9nUbk40fP55p06bx/PPPM3nyZEJDQ3FzcyMoKMim5UCbXUHppKQkgoKCGixQ27t3L4sWLWLcuHFMmzatQU/g2LFjLFq0iC5dukhrVXJzczEajdIXXqVS4e/vT0BAAAEBAbi4uGC1Wlm+fDm5ubkEBgYyceJEMjIyOH/+PPb29vj7+xMSEoJWqwWun6tzo/bs2cPy5cvZvHmzdMxqtUpd7jp1Ac9isUi5BXZ2dndtPs7dxmKxNMj5qRsQr+vZXfveymSyehnh194Pro652NnZNcj1uPZx19arufb/1e/b8kftqDvX79tVd77rvaab1eyCyfVUV1fz6aefEhwcTExMTL0FbHW/GN988w0jRoxg3Lhx0rWs2Wzm9OnTbNiwQUqaq6qqwmw2S7VdnJ2dOX78OCUlJQwePBiTySQFEE9PT5ulsJvNZl544QV8fHykZKo6Op0OuVyOk5OTCBjCbdMgmBQUFJCdnd3g16w5slgsnD59mu+//55+/frxwAMP1OuqlpWV8eabb+Lj48M///lP5HI5ZWVlFBQUSFtZKBQKaWW0h4cHvr6++Pj4oNFosFgsVFVVUVVVVW+Q7Vbk5uYyceJEvv/++3o5JQCfffYZnp6eDBs2zOazU/cqJycn2rVrJ9Yj2VCDYLJr1y6+/nG6qVIAAA9eSURBVPprampqGqtNd73KykoSEhIICAggJCSk3m1ms5nz589TXFxMz549CQkJwd/fH39/f9RqNXq9nuLiYqqqqigpKeHy5cvk5uZSUlIibftwO6rSHT16lODgYHx8fBr0TrKysjhz5gxKpZLu3btfdxyqqQkKCmLRokXN4rXeKeIy5xaUl5ezZMkSHn744Xq5GEajkUOHDrFz5048PT159tlnpV6C1WqluLiYuLg4Lly4QKdOnVCpVBgMBvR6PTU1NQ1yXGxZle6pp55i2LBhjBgxot71ekZGBj/++CMXL17k0qVLvPfee/UyjwXhRt3zszmNwc3NjX/+858Ndomrra0lJyeHbt26MWTIEDw8PKTbysvL2bp1K4mJifTp04e+ffvi4OCAXq9Hp9OxY8cOfvvtNzp16kR+fj4mkwlnZ2fUajUuLi71KtK5uLjcdHBxcXFpUHS6pKREquE7ZcoUPvroI9HtF26ZCCa36HrbTarVakaOHIlKpaqXxWswGFi/fj0pKSmMHTuW+++/X+peq1QqDh48SEJCAiNHjqRHjx7Y2dlJC/eKiopITk6WMoNVKpVUtNvd3f2Gq9LpdLoGS8tTUlJYtmwZPj4+fPPNNxQUFDBhwgQbvDtCcySCiQ3J5fIGg59wNYclOjqaPn360KZNGyk/wGg08sUXX/DTTz/x8ssv07FjRykIWSwWCgoK2LlzJzU1NUyePFkqsZiTk0NGRoa0pYiLiwuenp5otVopzf5ap0+fxmAw0LJlSynoVFVVkZ+fz6BBgxgwYABnz57lwoULTabolHDniWByB9Qt5//9PP62bdvIyMjgv//9L23atKnXu8jOzubDDz/E3t6eWbNmERAQINUsKSkpYcuWLSQnJxMZGUlFRQXZ2dnY29tjb2+PSqUiMDAQX19f5HI5q1evpnPnzvVKQej1evLz8xk8eDA9e/Zk//79DB48GC8vrzv63ghNhxiAbUR1CUS/H6dITExk8eLFtGvXjlmzZtX7gut0OlatWsWvv/7Kv//9bymDtaCggPT0dE6cOFGvrILJZMJqtRIREUHbtm2luiiFhYV89dVXdOzYEZPJRFpaGuPHj7/l4tSCIILJXSgjI4PS0lJCQ0PrTV0WFxfz1ltvkZeXx7///W/Cw8OB/7+kwNy5c1EoFHzwwQfodDpyc3O5ePEiRUVFUmmFur1vvLy8OHHiBG+88QZDhw7lP//5j5R+LdwZpaWlUipAUyCCyT1k586d7Nu3j1deeUVaDmAymTh48CBvv/02Dz30EDNmzECtVmM2m8nLy2PDhg2kpaUxevRo3NzcpKp0dduP1FWwqwswbm5u0g4Bd1NVuqZo1KhRDBs2jGnTpknLPK6dAbzXiDGTe0hMTAz9+vWr90tmNBrZu3cvTz/9tJRDYjKZOHv2LOvWrcNisTBr1izCwsKky6n8/Hz+97//UVpaSvv27TGbzVJVOnt7e2l717o6L3XJdI1Rla45sFgsvPvuu0yfPv2eriEjgsk9RCaTNegSu7q68q9//Qt3d3fpi15RUcGePXtQq9VMmjRJ2nERrl4qbd++nYSEBAYMGEBMTAw1NTWUlZWRlZXFrl278PHxwWg0kpqair29vZRIp9FocHFxwdnZGWdnZ5E9aiMymYzhw4fTunVrMjIyuHjxIkajUaqP8sQTT0glK65cucKmTZuAqwXDevfuLZUraGwimDQBv5+BUSgU9OrVi+Dg4HoftOrqat5++20qKip48skn6dKlCw4ODjg5OVFQUMAvv/yCyWSiW7duBAYGotPpKC8vJy8vjxMnTkhV3uqycuuS6OoS6sS6n1tjsVh4++23Wbp0KZWVlSxcuJDo6Gj8/PzYsWMHLi4uTJ06FZ1Ox8cff0x2djbh4eH8+OOP6PV6xo4de1dsUieCSROkVquvu7WBnZ0dQUFBDBw4sN7Wo0lJSaxevRo3NzemTJlCWFiYtCz9/PnzbN26FY1GI3XBS0tLKSkp4dKlSzg6OqJSqaSqdHWJdLaoStdcubq6MmrUKPr27YuPjw9xcXFMnTqVU6dO8dNPP7FhwwYCAwPZuHEjP/30E7169WqwRqwxiGDSjDg4ODB16tQGVd7Onz9PREQEQ4YMwdfXV6qtkZWVxapVq/D19WXkyJG0atUKi8VCTU0NZ8+eZc6cOYwaNYqAgACKiorIy8tDLpfj6OiIo6MjHh4eUkU6d3f3u3ajtLtN3eZydf9dd7lTVFTEmTNnpP11ysrKcHZ2/tsrzm1FBJNm5vfdYXt7e2JiYrCzs6tX78RoNDJz5kwmTpzIqFGjUKvVUh3Tc+fOMXfuXEaNGsXUqVNRKpWYTCYMBgPnzp3j8OHDODk5UVhYyMWLF5HL5SiVSqnmS10JBrHB142p2y8HICQkhFWrVkl/Ozo6ijET4e4gk8muu1+xUqnk7bffJjw8vN4Mzvbt21m8eDHPPfcckyZNkm5zdHTk7NmzvP/++3Tu3JkpU6Ygl8vJzc0lNzeXvLw80tLSSEtLQyaToVKp8PX1larS3ezm681Rjx49cHJyIiUlheHDhzd2cxoQwUS4LrlcTkRERIPjeXl5LF++nKioqHolBQ8fPszy5csZMWIE48ePl2ad3NzcaNOmDb/++itff/017dq1o3379pSWlpKdnU1GRga1tbU4OTkRFBQk1dStW7xoZ2fXZFcyu7m5Se9T3RiT2WzG1dVVes0KhULKPfH39+eDDz6ot4HdmDFjeO211+6KzGWRtCb8bVlZWXz++edEREQwZsyYemMjBoOBQ4cOsW7dOvr168eECRNwdHTEZDJx5coVjh49ypkzZ2jbtq20jUNdycu67V29vb1xdHTEwcEBhUJxV+8f3ZyJYCL8bWazmaqqKunLfq3//e9/rF69usG+0hUVFezatYsffviBBx98kHHjxmE0GikuLiYvL4/ffvuN6upqaRW2q6srnp6eeHp6otFopDIPKpWqyfZc7jXiMkf42+Ry+R/mOdjZ2TFv3jyioqKkY/n5+Wzbto1jx44xbtw4qdvu4uKCq6srly9fJicnh7CwMDp16oTJZKKiogKdTkdOTg7V1dXSFHTHjh2lyv5C4xLBRLitHn744QbHzGYz9vb2TJ8+nS5dukjHKyoq+OGHHzh8+DA9e/Zk6NCh0sBsZWUlWVlZxMbGolarCQkJQS6XIzrWdw9xmSM0iqqqKhQKRb39ZM6dOydtvt6jR496RZ6ysrL473//i1ar5ZFHHqF169bA1VknMcV8dxDBRLhr6PV6SktL8fPzqxcgEhISWLBgAb179+bxxx+/K2YuhIZEMBHueqtXr6a2tpYJEyZcNydGuDuIYCLc9eqq6otZm7ubCCaCwNV8mLoSDyKH5daIYCI0G1lZWZSUlEgbeXt4eEgbjs2ZM0faD8nV1bWRW3pvEsPgQrMxf/58jh49SkhICDU1NWi1WhYuXEirVq0au2lNgggmQrPy+OOP8/LLL5OXl8err77KmjVreP311+vdR6fTERsbC4BWq6VPnz54e3tz9OhR7O3tSUlJQa/X4+DgwFNPPSU97sSJExw7dgy4urq3X79+zarsgggmQrPk6upKaGgoly5danDb66+/jqenJ9XV1ezbt4/CwkKeffZZtm3bRkJCAj169ECpVLJu3Tpat27NQw89xJkzZ/jqq6+QyWT4+voSHx+Pi4sL0dHRjfDqGocIJkKzVFxczIkTJ677Ze/WrRuPPfYYlZWVrFy5kl9++YWpU6cC4OHhwcyZM/H398dsNrNt2zZ69OhBXFwcdnZ2zJ8/Hw8PDxYsWEBsbKwIJoLQVK1atYr4+Hjs7e3p3r07jz32WIP7BAQE0L9/fywWC/n5+URGRlJTUwNARESEtA6pZcuWHD9+nJqaGkpKStixYwdnzpwBrpZquN5+1E2ZCCZCszJy5EiefvppaV9ojUZT7/YzZ87wj3/8g1WrVuHt7c2OHTs4derUH57v2ipoMTExzJ49W/q7uVXvF8FEaFa0Wi333XffH95eXV3NlStX6Nu3L8XFxaSnp//lOd3c3OjUqRMbN26kqqqKDh062LLJ9wyxo5LQbKjV6j/citPZ2RknJye6dOnCCy+8gJeXF9HR0ej1elxcXKRSk9cmtTk6OuLq6opMJmPs2LF0796dhx56CK1Wi1ar5a233rqTL6/RiaQ1QRBsQvRMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBEGwCRFMBOEaGzZs4OTJk43djHuSCCaCcI2ioiIMBkNjN+OeJEoQCE3e+vXrUavVxMfHU1FRQcuWLZk5cybLly8nMzOTQYMGMWrUKJRKJZWVldjZ2VFZWcmyZcsIDQ1l586djBw5EpPJhIODAz///DOlpaV8+eWXFBYWsmTJEsrKygCYMmUKffv2BWDBggUMGDCAL774gtDQUObOnduYb8NtJ4KJ0OQlJCQQFxfHvHnz0Gq1zJo1i6SkJGJiYnB1dSUuLo7WrVtz//33s2vXLry8vIiMjGT16tVERUUxffp0QkJC+OKLL9i2bRsvv/wyvr6+VFVV8eKLL6LVannsscdISEjg008/RaPREBUVxY4dO9i6dStvvfUW7u7ujf023HYimAjNwuDBg4mJiUGj0dC9e3d8fX2ZOHEiRUVFpKenk5ub2+AxGo2GCRMmMHDgQOnYwIEDiYmJQavVcujQIY4fP86hQ4fw8PAgIiKC2bNnk5ycTPv27QGYOnVqvcc3ZWLMRGgWtFqttBm6Wq1Go9GgUqlQKBTodDrKy8sbPMbBwQFPT896xzw9PaXtK6qqqggICMDDwwMAX19f3N3dyc/Pl2rG+vv7386XdVcRwURo9qxWK7dSI0wul5OTk0N1dTVwteJ9RUUFWq22We2XU0cEE0G4RT169CAkJIT58+dz+vRptm/fjlqtpmvXrigUisZu3h0nxkyEJi80NBRXV1fkcjkA4eHhaLVaABQKBR06dJC2pejWrRv+/v7SVhh1lzAA9913HwqFQrpccnJyYsWKFTz99NMkJibi6+vLzJkziYyMBCA6OhpfX987+VIblagBKwiCTYjLHEEQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbEIEE0EQbOL/A6nXH397j7udAAAAAElFTkSuQmCC)
Physics-General
Physics-
PQR is a right angled prism with other angles as 60o and 30o. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
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)
PQR is a right angled prism with other angles as 60o and 30o. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
![](data:image/png;base64,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)
Physics-General
Physics-
A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror
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)
A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror
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)
Physics-General
Physics-
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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)
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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)
Physics-General
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
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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,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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,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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