Physics-
General
Easy
Question
A thin prism
with angle
and made from glass of refractive index 1.54 is combined with another thin prism
of refractive index 1.72 to produce dispersion without deviation. The angle of prism
will be
The correct answer is: ![4 to the power of ring operator comma 30 to the power of ´](data:image/png;base64,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)
![fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction](data:image/png;base64,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)
Þ A' ![equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent](data:image/png;base64,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)
Related Questions to study
physics-
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if
. The index of refraction of glass is
![](data:image/png;base64,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)
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if
. The index of refraction of glass is
![](data:image/png;base64,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)
physics-General
physics-
Which of the following diagrams, shows correctly the dispersion of white light by a prism
Which of the following diagrams, shows correctly the dispersion of white light by a prism
physics-General
physics-
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
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)
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAADFCAYAAAC1rAWTAAAgAElEQVR4nO2dd1iT1/v/XxkQEBUHuK0bbR2tWmvVarWfWqu1UFdrrYpVENyouC3VOhBF3LNurVtRcbZ11VXrqtaJew9UBGUkJHl+f/hLvowkJCEkQZ/XdXGZs8+DeXPuc859ziMRBEFARETE6ZE6ugMiIiLmIYpVRCSPIIpVRCSPIIpVRCSPIIpVRCSPIIpVRCSPIIpVRCSPIIpVRCSPIIpVRCSPIIrVhmg0GjQajaO7IfKGIorVRjx8+JB9+/Zx9+5dR3dF5A1FFKsNSElJYcqUKURGRqJSqRzdHZE3FFGsNmDNmjX8999/jBgxAh8fH0d3R+QNRRRrDtm3bx9Lly7F19eXpk2bOro7Im8wEvGInPXcvn2bgQMH4ubmxuLFi3F3d3d0l0TeYOSO7kBeRalUsm7dOlJTU4mIiBCFKpLriGawlWzZsoWYmBh69+5NlSpVHN0dkbcAu4k1JSXFXk3lOsePH2f27Nk0a9aM1q1bO7o7Im8JORLrlStXOHHiBElJSdnmHT9+PDdu3MhJc07Bo0ePWLBgAUWKFGHIkCGO7o7IW0SOxDplyhQmTZrEs2fPss0bFRXFqFGjOHToUE6adChKpZLNmzdz+/ZtJk+eTIECBRzdJZG3CKvFumrVKrZs2cKtW7fMcgQQBIHSpUsTFRXF6tWr0Wq11jZtNwRB0JvvgiDw+++/s3DhQoKCgqhataqDeyfytmGVWO/fv09sbCzu7u48evSI5ORks8qFhoby5ZdfsmrVKgYPHsyDBw+sad4uaLVa7ty5w/HjxwGIjY0lMjKSxo0b8+233zq4dyJvI1aJdenSpTRs2JD27dvz8OFDXr16ZVa51NRU2rVrR69evbh27RohISF6MTgbarWaf//9l8uXL5OcnMz8+fMpUKAA48aNc3TXRN5SLBbr1q1b0Wq11K1blypVqiCRSLh165ZZZSUSCUqlko8++oiff/6Z0qVLM2nSJNatW2dxx3MbtVrN7du3uXnzJtu2bePEiRNMnjyZQoUKObprIm8pFok1Pj6eU6dO8cknn+Dt7Y23tzcFChTgypUrZq0I61Cr1ZQuXZqQkBBatGjBypUrGTVqFAkJCRY/QG6hVqs5e/YsGzZsICIigi+++IL33nvP0d0SeYuxSKzLly+natWqfPbZZwDUq1ePYsWK8fDhQ5RKZbblJRIJEokEeD0ndHFxoU2bNnTv3p2LFy/StWtXzp8/b8Vj2B61Ws3Fixe5efMmycnJNG7cmISEBE6cOMGmTZuc1nwXeXMx293wv//+Y/Xq1cTHx7Ny5UrS0tJITk7m5s2bVK9e3Syx6pBIJAiCgCAIaDQaGjRogLe3N6tXr2b48OEEBQXx9ddfW/VAtkKlUun/cDx//pwxY8agUqn48MMPad++PWXLlnVo/0TePswSq1Kp5M8//6RNmzZUr16d1NRUAAoWLMjgwYM5fvw4iYmJlCxZ0uyG0wtWEAQqV67MwIED2bt3L/Pnz+fSpUsMHDgQFxcX654sB6SlpbFt2zb9wtmLFy9ISEigQ4cOtGnTBh8fH+Ry0a1axL6Y9Y1bunQpjx8/ZvDgwXh7e2dIW7JkCRs2bODly5fZ1qMzgdOHdYd+tFotBQoUwNfXFy8vL5YuXcqxY8eYNm0a5cuXN/d5bMLFixcJDQ0FwNvbm+7du9OpUyd8fHxwc3Oza19ERHRkO2eNjo5m06ZNNGnSJItQAb0T+6lTp0hLS8u2wfTz1sxhrVaLRCKhUaNGDB48GE9PT4KDgzl48KDZD5RTkpKSGDlyJOXLlyc0NJQdO3YwYsQIatWqJQpVxKEYPc967do1xo8fz4YNG0hOTqZAgQIMGzaMkJAQPDw8iI6OJioqin/++QeVSoVMJmP48OEMGzbMoBuem5sb165dQyaT6eMyN60L6wQcHx/Prl272LNnD99++y0BAQG2fPYspKWlMWXKFHbt2sW6devIly+fuFUj4jQYFWtqaip37tzh1atXuLi4oFQqKV68OKVKlUImk/Hs2TPu37+PVqtFJpORlpaGt7e3Pj0zOrHK5fIMIjUmWACpVIparebIkSMsXLiQypUrM3HiRLy8vGz1/Bna3b59OwEBAWzdupWPP/7Y5m2IiOQEu90UkV6sOnRNG+pC+lFWEAQuXrzIvHnzUCqVhIeHU6tWLZv2786dO3zyySeEhIQwaNAgm9YtImIL7CrW69evZxl1zRlldYJ99uwZ69at49ixYwwaNMhmZ0m1Wi0dO3bE1dWVpUuXOmQFWkQkO+y+/5B+BThz2FiaLs7Ly4vg4GC9OXz69GkGDRpE/vz5c9SnadOmce3aNQ4fPiwKVcRpsevIeuPGDf3Iasr0NZUGr0V87tw5xo4dS+nSpZk6dSrlypWzql/79u3jq6++YseOHXrPLBERZ8TudzDptmkyb+GYmwavhVurVi3mzp2Lp6cnAQEBnDx50uK+JCYm0qdPH8LCwsRrREWcHruPrLoFJnNXhLNLc3FxYe3ataxevZqePXvSpUsXXF1dzepTt27dSElJYdWqVaL5K+L0OMxnzpy5anZp8HpvtGPHjpQtW5YRI0Zw+vRpxo4dm+32zty5czl69CiHDh0ShSqSJ7CrGWzKe8nStPTxaWlpNGzYkJUrV3Lz5k0CAwO5du2a0X78888/DBkyhClTplCsWDGbPqOISG7hkHuDTc1HzU3L/FmtVlOmTBkWLVpEtWrV6NatG7t27criAqnVahkwYAChoaG0atUqS3siIs6KXeesN2/eNOgUYShsbpqhz/ny5WPLli1MmjSJbt26ERwcTJEiRQDo06cPd+/eZe3ateTLl88GTyYiYh/sOmc1deomfbogCGanGYpPTk7m66+/pmLFigwaNIhr164xYcIE9uzZw/bt29m5c6coVJE8h11H1lu3bhlcDc4ubCwtuzJyuZzk5GQmTZrElStX+Ouvv1iyZAldunQRz6OK5Dkc9q4bU3PTzGFT+7GmyqjVatzd3Rk/fjxJSUkUL14ctVpt1tlbERFnw+6rwZaGsxOmqTJSqRRBEBg1ahSenp6Eh4czYcIExo0bx927dw16SomIOCsO82AyFTbXsyk7jycXFxeio6OJiYkhODiYVq1asX37dm7fvs2gQYO4cOECGo3GZs8mIpKbOGzrxtieavo4Y2FzPru6unL16lVmz55Nv379+Oijj1Cr1RQpUoTFixdTrVo1goOD+e2335zqClQREWPYdYHpzp07Jo/IWRLO7tB6SkoK/fr1o1ixYgwbNoyCBQui0Wj0+Tw8PIiJiWHChAl06NCBnj178s477+TsIUVEchGnNIMzhw2NwsbipdLXjzRt2jTi4uIICgqicOHC+hdh6fIlJSXRsmVLlixZwsmTJxkzZgxnz5616bOKiNgSp/Ng0oWzy2Ms3s3NjV27dhETE0NAQABlypRBrVZnyat7lUelSpX49ddfKVy4MMOGDWP9+vVmv2hLRMSe2N0Mzry/aa0ZbOiz7mRP//79adasGQEBAbi7u+vFaqycRCLBzc2NNWvWsHLlSlq0aEFQUBClS5e27mFFRHIBu4r17t27WS5Mg5wJVheWy+UkJSUxZMgQpFIpYWFhFCtWTP/uWHMOuysUCk6cOEFkZCQ+Pj4EBwfzwQcfWPG0IiK2x2nN4MxhU04SUqkUiUTCnDlzuH79Ov7+/hQrVoy0tDSLDrsrlUrq1q3LrFmzUCgUjB8/npiYGHF7R8QpcGoPJnO2bwRBIH/+/Ozfv5+dO3fyww8/ULt27QwCs+RUT1paGkWLFmXkyJF8/PHHTJs2jbCwMOLi4qx8UhER2+BwR37IeIth+rAuztTBdN2tiUuWLOHLL7+kXbt2yOXyLPPU7A4JpK9TrVYjlUrp0qULpUuXZsGCBTx//pw+ffpQo0YNm/wuREQsxSFbN9k5RZjarkkflsvlJCYmMnnyZKRSKT/88AOFChVCo9Fku8VjrE7dj+4Nd5999hmTJk1CKpXqT+6IiDiCPOMbnDmPRCJBJpOxYsUKzp8/T5cuXShfvnyGV09aYv4aShMEAbVaTcWKFQkNDaVWrVpMnz6diRMnkpiYaNYzi4jYCqe4NxgsM4XhtQfSwYMH2b59O+3ataNp06b6eWpms1ZXn6m2TaWlpaXh5uZG165dKVGiBGvXruXu3bsMGjRI/2IuEZHcxq5bN/fv3zf7pghTYYVCwd27dxk9ejSlSpVi6NChFChQIMsVLra4iSJ9WLfqfP78edatW0dSUhLBwcE0adLE+IOLiNgIpzeDM4dlMhmvXr1ixowZPH36lM6dO1OkSBHUarXVhwHMTdNqtWi1WmrWrMnAgQOpXr06kyZN0r+DR0QkN8lzvsGurq5s3bqVEydO4O/vT7Vq1fRvYre0PmvSdPPYokWL0rlzZ9q0acOGDRsYOHAg9+/fz/b5RUSsxWmcIkytBuvIly8fZ86cYfPmzXz11Vf4+fnpHfQtqT99HmvT1Go1CoWCVq1aMXDgQOLj4xkyZAinT582+ewiItZi1znrgwcPrPYNdnFx4dGjR4wZMwZBEAgPD6dw4cJ6d0JL6zMUtiZNJ+i4uDiio6M5fvw43bt3p127dgb/4IiIWItDL/nWxWUXlkqlpKamsmjRIi5evEhAQABFixbN4E5oSX3GwtZu72i1WooXL07Xrl3x9fUlIiKCYcOGER8fj4iIrXAaM9hU2N3dnaNHj7J3714CAgKoV69ehhE1p/NgQ84RlqbpLmf76quvGDFiBOfPnyckJITr16+b+E2IiJiPU/kGGxKCQqHgwoULLF68mCZNmtC5c2eDjvU5cbAwFLYmTaPRIJPJqF+/PhMmTKBIkSL07duXv/76K0t/RUQsxWFihewFJJfLiYuLY968eSQlJdG3b1+kUmmGWx9M1Wet2Z2TNN1ctkSJEvTv358WLVrQv39/pk+fLh5qF8kRDnXkTx9vyHsoLS2NjRs3cuDAAWbOnEmJEiVQKpVGPZRM1WdpWFenpWm6sEajQaFQ0K5dO8qUKUNERASxsbGMGTNGfBmWiFU4zJHfUHx6FAoF58+fZ+PGjQQFBdG0adMcz1NN9cNW2zvp4wVBQCqV8vHHHzN37lwSExPp0aMHsbGxWZ5fRCQ7nGbOqouTSF6fprl58yYzZ86kevXq9O3bVy9Uc81UY2F7mMWG8pUqVYrw8HA++ugjOnTowIYNG7K4R4qImMLh51kz719KpVISEhL49ddfuXjxItHR0RmuEM1czpSZaihsrIytzeLM7epG2e7du1OhQgVCQkI4d+4cw4cPx8PDI7tfnYiIc7gbpjcdtVotBw4cYNu2bUyYMIF33nnHoN+vsTpMtWNp2Fqz2FS8IAg0a9aM9evX8/fffxMYGMiLFy+MPpuIiA6nuJFfFyeTybh+/Trz5s3D39+f1q1bZzmfao5gLAnnZPXYUsHqPguCQLly5Vi1ahXFihWjRYsWHDp0SLzryQD79+/H19eXGzduOLorDsfhWzc6pFIpjx8/ZurUqXh5eTF06FBSUlKyFZC9563ZtW9JmbS0NEaMGIG/vz9t27Zl/vz5GQ4lvO28ePGC0NBQatSogbe3t6O743AcvnWji0tJSWH16tUcOHCAXbt2mZynGqrDnvPWzGFzPhsrk5aWRps2bahcuTJDhw7lypUrjB8/noIFCxp81reJsLAwKleuTJ8+fShQoICju+NwHD5n1cWdO3eOZcuWERkZSbVq1bL1UsrtEdOaOi1ZHU7/WaPRUL16daKjo3n+/Dnt27fn/Pnzb7VZvGjRIo4dO8bIkSPFy9b/Pw73DZZKpdy9e5fx48fTtm1bvvvuO70paGp7J/NnQ3WbG87JvNVYPzPHmzOPdXFxYdq0aTRu3Jivv/6adevWkZKSYrDuN5mTJ08SHh5Ot27dqF69uqO74zTY9YjckydPMhyRk0gkxMfHExYWxpUrV9i9e7d+RTg9pm7TtzZsizqM1WnO7f+m0lxcXPjrr78YNmwYnTt3ZtCgQRQqVChLuTeR5ORkvvvuOypUqMDPP/9M0aJFHd0lp8GhThFarZYtW7awdetWpk+frn+1hq1MXFuPmObUmV1b5qSlpaXRuHFjoqOj+ffffwkODubmzZsGD9q/aYSHhyOTyejTp48o1Ew47A4miUTCtWvXmDt3LlFRUdSuXTvDxdy2EKi5ZWxZpyWmr6k0tVqNt7c3v/76K2XKlKFDhw5s3rz5jTaLV69ezc6dO+nVqxdVq1Z1dHecDodcRSqRSHj48CGDBw+madOmdOnShaSkJKP5LVmlNbdMbq4eZ171tdYbSqvVIggCQ4YMoXLlygwYMIAbN27Qo0ePN27UOX/+PFOnTsXX15emTZs6ujtOiV3nrHFxccjlclJTU/npp584ePAg+/fvx8PDw+QVKobibDEHtaaMva+N0X12cXHh0qVLhIeHU6FCBYYPH0758uWzPE9eRKlU0rdvXwB++eUXSpYs6eAeOSd2n7PK5XJ27tzJ5s2bWbBgAZ6enlm+qObMA03t2Zoqk9vz1pyYvqbS0tLSePfdd1m4cCEAQUFBbN++/Y24AjUqKoq7d+8SFBQkCtUEdhWrXC7nypUrTJ48mXHjxtGwYUOjfr/WbIfo4pxp3mrLtLS0NFxcXAgLC6Np06aMHDmSefPm8fTpU/Iq0dHRbNy4kY4dO/Lhhx86ujtOjV3N4CtXrtCjRw/Kli3L0qVLsyyWGOtKduarueXeBLNYd3pHKpVy+PBh5s+fT+3atQkODqZSpUpZnseZiY2NpW/fvtSoUYPx48eTL18+R3fJqbGrWHv16sXu3bvZs2cPxYoVM0ssxuLNLetsAs0ctjYNXu/H3r9/n9mzZ5OUlERAQABNmzbNct2rM5KSkkJYWBiPHj3Sn64SMY3dzGCJRMLWrVtZvny53n3MXDPWUF5zTFND+Rw9b80ctjYNQKVSUbp0aUaPHk3lypX55ZdfmDNnTp64AnXhwoX6O5ZFoZqHXf8Eu7u7Ex8fj0ajwcXFRX/vr6HRzlC8OXHm1pfT7Z3sylhSX07SVCqV3mp55513WLNmDY8fPyYgIICKFStm+T04A3v37mX16tW0b9+eZs2aObo7eQa7msGDBg3iyJEjNGvWTD93TX8k7E0wi3Nan7VpEsnr63AuXrzIihUrkEgkdO/enUaNGmXpjyO5ffs2I0aMwNPTkylTppA/f35HdynPYFexvnz5ko0bNzJv3jw8PT0ZPnw4jRo1QqVS6V3prBWdsXhbiTgvzGMFQcDd3Z24uDiWLl3KyZMnadu2Lf7+/k4hiqSkJCIjI/nvv/+IiIjIcwtijsauWzdpaWl07NiRyMhI3NzcCAsLY/ny5ajValxdXQHjc0pj80Rr91bNmXeaas9Y2Bb15SQtNTWVIkWK0Lt3b7788ks2btzI5MmTuXfvnpH/FfsRHR3Ntm3b6NChgyhUK7DryPrs2TPkcjmurq7ExcWxfv16NmzYQOXKlRk+fDhVqlTR3w6hIy+OtLldnzlpUunrv8OnT59m/fr1+nntBx98kKVv9uDIkSP8+OOPeHl5sWLFCipXruyQfuRlHOLIr1KpKFq0KMHBwQwZMoR79+4RFBTEnj17cHd3RyaTZSljqJ7s4gzF28ORIjfqszRN51f88ccfExISQsGCBRk+fDirVq2ym9eTWq3m6tWrzJ8/n5CQEK5evYq3tzdeXl52af9Nw64j6/Pnz/V7gLrVTN2iyJIlSzh16hS+vr4EBATg6emZYZTNyWhqKC63HClsPZdNH2dNmiAIKBQKEhIS2LRpE7t27eKzzz6jV69euXavUWpqKqdOnWLJkiWcOXOGBw8e8PjxYwAGDx5MZGRkrrT7puPQ86yCIOh9XsPCwggICGDr1q106dKF8+fP4+7uniG/OaOksXhz9mmN5cuunLV7rIbqM1W/NWm67Z38+fPzww8/0Lt3by5cuEBYWJjNbwwUBIHHjx8TExPD4cOHkcvleHl56YVaokQJ3n//fZu2+TbhsJFVh655mUyGIAgcPnyYOXPm6I/QtW3bFrVaneGsqz3msebks+e8Nbv6zUnTWTK3bt1i9erVxMbG0r9/f5o3b55h6pETkpKSePDggX5VOiQkBK1Wi7u7O3fv3mXJkiU0aNDAJm29bTj0KlL4v7/+utsMmzRpwpQpU/Dz8yMyMpKhQ4cSHx+Pm5tbhi+doXrMiTMUb20+e85bM9dpaRqgt2QqVKhAcHAwjRs3ZsSIEUybNo1Xr15hCzw8PKhSpQr58uVj3bp1eHl5sWnTJpo3b07hwoV57733bNLO24jDboowlCYIAhqNhnLlytGnTx+GDh3K33//TYcOHTh9+jTu7u5Gv5Cm4uxpFuemQDPnsSQt/WeVSkWhQoX4/vvvGTRoEHv37mXkyJE8efIEW6BUKlmzZg0xMTGEhYVRrFgxPDw8KF68OJ6enjZp423EKa4iTZ+m++uvUCho1aoVUVFRVK5cmV69erF8+XLkcrnelM7JaKqLM3e12JJyuTlvtbQ9Y581Gg2urq589tlnjBs3DpVKRUBAAKdPnzY6LTCXEydOMHPmTAYOHKifo1aoUMFh20ZvCnads8bHx2eYs5pqWrdaLJFISEhIYNu2bcyaNYu6desyduxYSpcurV8tzsmqsLF4W8xjc9u10ZL2TOVzcXHh+fPnbNiwgRUrVjBy5Eh++OEHvaOKJTx48IDevXtTtmxZZs2apY+PjY3lzp07fP755xbXKfIah4oVshcsvF58UqvVHDp0iAkTJqBSqZg+fTofffQRSqVSv0Vhqg5z4m0hWHu4MlraB2PbO+nDMpmM5ORkDh48yNy5c2nevDmjRo2y6A13L1++JCIighMnThATE5NB7MnJyXrvKhHrcLhYwTzBSqVSBEHg1q1bzJ8/nwMHDtCjRw+6deuGQqHQrxbndD/WULw1q8/2Fqi57Zsqo1voe/DgAdOmTSMtLY0ZM2ZQpkyZLH3JjFqtZt26dQwaNIht27ZRv359g/03NQ0SMY1TiBXME6zuP1qtVhMTE8Po0aOpXbs2kZGRlC1bVu+Z4yxmcW4L0pL2LemXRCIhKSmJRYsWsWXLFqZPn06LFi30LoyGiI2Nxc/Pj759+9KnTx+j+USsx65iffHihf4ib2NYMsqeOnWKsLAwXr16RWRkJA0bNkSlUjnULHa0QDPHmTvCZk6TSqUolUr++OMPwsPD6d27N4MGDTK4H5uQkEBQUBAeHh4sXrw4S7qIbXCIWME8UZpK042y8fHxzJ07l/Xr19OtWzd69uxJ/vz59S91yqlZbAsT2FCcI81iS/64aLVabty4wfjx4yldujTz5s3L4FmmVCqZOnUqGzdu5ODBg+Lb3nIRh4kVci5YeC1amUxGTEwMISEh1KlTh6lTp/LOO++QlpZmsi5bm8W2FqQt27DWXNd9VqlUTJkyhePHj7NgwQLq1auHVqtlz549fPvtt2zfvp1PP/00S39FbIfDX6Zsal/UnD1TQRBQq9W0bt2a7du3o1ar6dixI3v37tUvaOTEh9hYvLUOFNmFc8MLypTfcHb90P3r6urK8OHD6dy5M//73/9YtmwZr169YsSIEfz888+iUO2AQ0fW9FgzyhqKl0qlzJgxg5kzZ9K9e3d69+5NoUKFLL6JwpK8jhwxza3T0pHUWJogCJw7d47Ro0ejUqmoUaMG69aty9K2iO1xuG+wjuw8m8yN12q1hIaGsnDhQhYvXkxgYCD37t2z2E3RVF5nGjHNrdMajydDaRKJhBo1avDNN99w48YNnjx5QmxsLCK5j9P4BuvSLTWLDcUrlUqaN2/O4cOH8fDwoF27dsTExJCammpRPab6nBOf3pyEc1KHLQQrlUo5e/YsU6ZMYc6cOXzyySc0adKELVu2mLSORHKOXc3ghISEbLdudNjCLJZIJLi6ujJnzhzCwsLo3r07ISEheHl52XV7xxnM4pwuMMH/7b9+//33NG3alNDQUFQqFQcOHCA8PJyuXbsyZMgQmx23E8mIQ8SqI7umbTWPVSgUHDp0iODgYCpWrEhERATlypXT/+Gw9TzWXqLOybzVmjS1Ws3IkSN5+PAha9eu1e9py2Qy7t+/z5gxY/D09GTSpEmUKVNG9FayMQ5fDc5JurlllEoljRo14vDhw/oXE69evZqEhARkMlmOzWJD80dz8jhy3mpN2tq1a4mJieGXX35BpVLp0zQaDaVLl2bmzJkUKFAAPz8//vzzT/1et4htcOjIqiMnZrElo69UKsXFxYUlS5YwdOhQvvvuOwYPHqx/nYduxdicNszpj7V7trk9Cpuqz9gK+4ULF+jUqRNjx47F19c3y+q6ILz2etJoNKxbt45FixYREhKCv79/BicKEetxCrHqsNYsttRcVigUnDp1isGDB+Pq6srIkSP54IMP8PDw0N9YYW3bttruMSePPeaxEomEV69e4e/vT926dRk1alSGK3YM1SOTyTh9+jTTpk2jVq1aDB06lOLFi2d5PhHLcJqtG7DeLLZ020epVPLBBx+wZ88e6tatS1BQEHPnzuXx48e4uLgYdFi3ZFXYWgeK3F49tmblWK1WM378eP2WmEajybYetVpNvXr1mD59Oo8fP8bf3599+/bpPcpErMOpRlYd9jKLdavF69evZ+jQoTRr1oxBgwbh4+ODVCrNMoKYasPa0dOcfLYehc2tz9XVld9++42xY8eyatUq/a0Ppkzm9GlyuZyUlBRmz57Nnj17GDp0KG3btnWKV3nkRewq1sTERLO3bsC61WBr0hQKBVeuXGHMmDE8fPiQwMBAvvzySwoVKqRfSDG3DWuEZm253BCoDldXVy5fvoy/vz/9+/enffv2RuszVbfOSvnjjz9YtWoVjRs3pmfPnqJZbAUOESuYN3pml8+WaXK5HK1WS2RkJEuXLuXrr7+mV69eVK5cGaVSaXDxyRnmtsiJXWQAABTOSURBVLkRlslkJCYmEhAQoH/vq0QiyfI7sOSPQb58+bh8+TLTp09HLpfTq1cvGjRoIO7JWoDDxAq2EWx26ZaaxTKZjN27dzN27FgqVqxI//79qV27Nq6urmaPsjkRrDn5cjoKm8ovkby+02rkyJGcOXOG5cuX4+3tbdT0Nbde3d3BcXFxzJgxg0uXLhEUFISvr69oFpuJQ8WqIydzVHPSrZnH3r59m8jISE6fPo2fnx/+/v4UL16clJQUs9uw5zw2uzzm1pc/f37WrFlDWFgYM2fO5JNPPrGovuzmsS4uLqhUKjZs2MDu3bv54osv6Nq1K8WKFctSTiQjTiFWcD6z2MXFBaVSyaJFi1iwYAENGzakX79+1KxZE5VKZXDD31rBmhuX2/NWhULBtWvXCAwMpFOnTnTu3Fk/0lpanykxS6VSFAoFx48fZ9myZXh5edGjRw9q165t8uqYtx2nESs4n2ClUilSqZRDhw4xY8YMtFot/v7+tGjRAnd3d/3BgOzqcTaz2Ng89eXLl/To0YOSJUsSHh6Ou7u7wX3nnApW99nDw4ObN28yd+5c7t27x48//oivr6/oRGEEpxKrDmc0ix89esScOXP4448/aNKkCf369aNs2bKkpqZavXhkKN5RgnVxceGnn37i0KFDzJ49m6pVq2ZYUMrOvLUmTavV6r8Xy5cv5++//6ZVq1Z06dKFokWLZin3tuOUYgXnEiy8/jKnpqbqXekqVKhA3759+fjjj0lLS8vWq8dUvL3MYkNpgiDg6enJpk2b+OWXXxg1ahQtWrTQm7+2MrNNmcVyuRyJRMJff/3Fxo0bKVOmDMHBwVSpUiXL873N2FWsL1++tHip3haizS6PuWk6s/jMmTMsXryYq1ev0q5dOzp16kTBggVJTU01u35nGWkVCgVXr16lT58++Pr68uOPP+Li4pJlTp7booXXi1sXLlxgyZIl3Llzh759+9KyZUtcXFwQcYBYLXGKSI+zjLQ6s/jZs2csXryY9evXU7t2bUaMGEHFihUNmsWm6rd2BDUnX3ZhqVRKUlISgYGBuLu7ExERgbe3t9GL5mwxkpv6LAgC7u7uPHnyhMWLF3PmzBnatWtHly5dxFsTcZBYwfzFpPQ4i2Dh/1aLd+zYwZIlS3Bzc6N37940a9YMQRAM+sFaIlhD8bYwl9N/9vDwYNy4cezatYsJEyZQv359tFqtTefDlgoWXjuo6A61b9u2jQoVKjB48OC33uvJYWLVYWnzziRYnVl87do1li9fzt69e2ndujV9+vShcOHCTmsWC4JAgQIF2LlzJxMmTKBnz560adMGqVRq9GK53BCsqTISiQQ3NzfOnTvHqlWrePDgASNGjKBhw4ZvrdeTw8UKuTPKmkrP3AdLRkFDaQqFgvj4eNasWcOyZcvw8fEhLCwMHx8fi1wVjcXbQrDpPysUCm7cuEG/fv1o0KAB/fr1I1++fNkuklkaTh9nLC27Mm5ubty/f5/ffvuNw4cPExgYaPUb7vI6TiFWyJ0R1lA+uVzOwIEDOXnyJAChoaH4+voaPGFjiWDlcjlpaWkcPXqURYsW8fTpU4KDg2ndujVSqTTHZrEtTGB4PWKpVCp69epFcnIyEydOpFKlSmbPU61pM6ejrFwuJykpib1797Jlyxbef/99fvrpp7duP9Zp3EVM3WxoLL+l+eRyOVFRUfz5558EBwfz/fff07dvXw4ePGhxG4bOcMpkMj799FMiIiL49NNPGTVqFKNHj+bFixe4ubkZrMPaq2PMzZc5XLBgQVatWsXdu3cJDAykYsWKGf5Q5fTqmOzC1twWqVarcXNzo3Xr1oSGhnLv3j06duzIpUuXrLLK8ipOI1Ydhv7TdHPD9D+6L03mazJlMlmGn8x5pk+fTs+ePfnuu+8IDg6mTp067Nq1y+SXyNw0rVaLWq2mTJky9O/fn59++okjR44QFBTEpUuXcHd3N/tgu7VXoJqK9/DwYO/evURHR9OlSxf9Ylh2z2VOu5YchDcmflNlBEFAq9VSo0YNQkJC8PHxoU2bNkRHRxu9judNw+nECmT4z5NIJGzevJly5crh4+NDhQoViIyM1ItYl08mk7Fu3ToaNmxIlSpVqFy5Mo0bN+b27dt64T5//pyEhAR8fHzQarVIpVJ8fHw4d+5chnZN9cmcNJVKhbu7O+3atWP+/PkUK1aMLl26sHz5cgRBMDgVMHc0NZTXnHy6eerkyZN59913+eabb/THAo3VYeubKtLnMRVvql6VSkWpUqUIDAykb9++TJ06lfDw8LdihHVKsQL6mxoWLVrEwIED6dSpEzt27KB79+6Eh4fz008/kZKSoh9p586di7+/P/Xq1WP58uVs27YNjUZDo0aNOH78OIIgUKRIEerUqcOiRYvQaDQkJiayePFimjdvrm/XVoLVXX/y3nvvMX78eLp27cpPP/1EaGgoiYmJKBQKs+vPqVkslUpRqVRERkaiVCrp1q0bhQsXRq1W58rVMebWYYm5nD6s0WjInz8/vr6+REREcObMGTp16sTjx4+zPP+bhNMsMGVGIpFw4sQJ/Pz8aNq0KatXr9anhYaGMm3aNH777Tc6duzI/v376d69O40aNWLy5MmUKlUKgMuXL/PFF19QpUoVfvvtN0qUKMGzZ89o0qQJ8fHxqFQq2rdvT3h4uMFNd2u2eAzFy2QylEolhw4dIiIiAoVCwfjx46lduzZpaWk5WlAyFJ85XKBAAVauXMmCBQvo27cvfn5+WdrN7YUlU2Fr92nh9e/24cOHLFu2jJiYGBYvXkyzZs2y9PVNwClHVolEglKp5MCBAyQkJPD5558D/3dV6IcffohEItGv6B47doxbt27xxRdfUKpUKbRaLRqNhmrVqlGrVi327dtHYmIiAEWLFmX37t3s27ePQ4cOMXHiRDw9PY32w1QfzY3XaDS4urrSrFkz1q5dS82aNWnXrh0LFiwAsGgea65ZrMPd3Z2jR4+yYsUKfH19ja585/bCkrE6s2sru35oNBqKFy9Or1696NevHwMGDGD27NlZnu9NwLxhzkaY+vJnRqPRkJycjFwuz7JE7+3tTcmSJYmLiwPg/v37ABQpUiRLWxUqVADgzp07VKpUCYCyZcvq82m1WpMLFBKJxOiIZizNULxWq0UikVC0aFHCwsJ47733GDVqlP7KTnd39yzbO5bUn34hRheWy+Xcv3+fSZMm4eHhwffff5+hrKEy6cOG2rImbKpOY58tSdM5ebRp04aaNWsyZcoUzp07x4wZM96o7R27j6zmCFYQBPLly0ft2rVJTEzk33//zVDWxcUFV1dXXrx4wa1bt3jx4oXRunVm9/379/VzNI1Go/8RBCHbPtlqhBUEAY1Gg0KhoGPHjmzbto1Hjx7RokULjh49anSENWc0zRyv+zIvW7aMp0+fMnDgQIoVK2azeaqpPlo6Cps7V82uThcXF959910iIiJIS0ujYcOGnD17ljcFh5jBuv9MUz8AtWrV4ssvv2TFihVs3boViUTCgwcPmD9/Pjdu3KBIkSKUKVOGypUrA+hN3fTcvXsXgDp16qBQKEyOkub02ZI0Y/GC8Pqwd82aNVm7di2ff/45LVu2ZNasWUb7YqlZ7O7uzu+//86+ffsIDAykQYMGGe6QsrVAranDWH2m2squH4Ig4O3tzfDhw2nbti1t2rRhzZo1RtvNS9hNrBKJhAIFCuDu7m7Wj0QiITQ0lJUrV/Lhhx/qtxq++eYb8uXLh6enJxUqVEAul1O9enU8PT05d+4cSUlJ+hXipKQkLly4QNWqVSlcuLBZfbTnKAvo3wiwYsUK5syZQ2BgIImJiTm6aNzV1ZWzZ8+yYMEC6tevT6dOnQx6UOX2iJldnabqy0kavN5T7tKlC1OmTGH27NmMHj2avI7dxCoIAk+fPuXFixdZfuLj4zP8pKSkEB0dzd27d/Hy8mLz5s2kpKSQnJzMX3/9hbu7OwULFqRx48YAfPvtt/j5+TFp0iT++OMPfZs9e/bk8uXLREREULJkSbP34nIiWEvL6Mzwr776iv3796NSqWjWrBl79+61eDSF16ujT58+ZdasWbx69YqgoCC9D645I7atBGlJnbmVJpfLadCgAbNmzeLixYu0bNmSGzdukFexqxmsUCgM/ri5ueHm5qYPAxkcteVyOW5ubri6uvLPP/+wY8cOWrZsSZMmTYDXX/jly5czZcoUAgMD9XPa3bt3c+7cOfz8/PRzOHOFZq1ZbI25rEsrWbIkK1asoGvXrrRr147JkydbZLZLJK/3VHfu3MmFCxcYPXo05cuXz3CQ3Nw+O3Lemrl8TtK0Wi0lSpRgwoQJVKxYkaZNm2b4g56XsOs+66tXr7LdZ9UJaufOnYwdO5bjx4/r006dOkX//v3x8PBg4cKFlC9fPsOKoClz01hb5mDtCZ+ctH3o0CEGDx5MhQoVmDx5MmXLltX/wTFWj6urK4cOHeKXX36hTZs29O/fn6SkJIPtWbtna+v9Vkvry8merEqlYs+ePSxatIhu3brRt2/fLG07M063z2pIcBqNhvnz5/Phhx9SsWJF1q9fn0GounI6cy/9j6VtWZPPkrmquXU2btyYgwcPUrhwYZo3b87mzZtNvhRKLpdz9epVZs+eTenSpQkMDCQ5OTlDvuxGPkP9cuS81VDY2jR4vVrcpk0bpk2bxtatWwkICODBgwfkFZxOrOnR+bNWq1aN9evXc+3aNVauXEmhQoXMdkDPDmc1i+G1Q8P8+fMJDQ0lODiYcePG6Q+0py8nk8l49eoVy5Yt4+rVq4wePdrovUXZfaGN9Ss35q3W1peTtLS0NKpUqcLUqVN5+fIl33zzDceOHTPaL2fCqcWqVCqpWLEiV69eZd++fVSqVMmmI2b6/OaUsWZhyZyy2dUbHBzMn3/+ybFjx/j22285c+YMarVaf/pIKpVy5MgR9u3bx7hx46hWrVqGN5NbKixz8+V0FM5JfTlJ02g0eHt7Ex4eTsuWLRkwYABr1qxx+sMATi1WHeaatemxRljmCtZa4VmbptVqqVu3Lrt27aJKlSq0adOGlStXkpKSgqurq94Lys/PDz8/P/08NbvnyBw21yzOrpytFpasLW9OmlarRaFQ0KdPH4YOHcrChQsJCwvTe8U5I3lCrNaOaI4yi3MjTaPRIJPJiIqKIjw8nClTpjBmzBjOnTvHrFmzkEqlDBgwAKVSqR9xs6vbHGEYyufoeWvmcE5Gb91W2cSJEzl9+jSBgYGcPHnSKc/I5gmxgnXCS182N9rKTnjWzFXNGbn9/f3ZunUrN27c4NNPP+XKlStMnTqVfPnyZfiS2crcNTefPeetmevLSVpKSgqVKlUiKioKLy8vQkJC2L59u9G3BjoKuzry2wJ7CdbZqVmzJnPmzGHcuHE0b96c999/H0EQDJ6TteWdTobicuteptyoz9QxPW9vbyZPnszmzZuZP38+Dx48oGPHjhQqVChLfxyBXfdZt27datY1kq6urhw+fJiVK1eybNkyXr58mSVPTrqdW49s7b6qtf2RSCR4eHigUqkyvCTLWtEZK5/T87bG0rPbb7WkvKn6JBLjb8JLH9bt1RcsWJCjR4+ycOFCmjRpwvDhw/nggw8c/mYAu4m1VatWZp/kFwQBV1dX/ftx3rRR0RG87b9DS55f9/1TKBQkJCTQunVr+vfvj5eXVy72MHvsJlYREZGckWcWmERE3nZEsYqI5BHsshr86NEj1q9frz9TqZvEFy5cmFKlStGgQQN7dENEJFvi4uLYu3cvT548wd3dnZSUFFQqFRLJ6yN3LVu2xMfHxyF9y3WxLliwgB07dqDVavUHwNVqNWvXrqVgwYJMmDBBFKuI05CSkkJsbCyLFy/mzp071K9fn+rVq/Pq1Sv27NnDtm3bmDRpkv7SPrsi5CLjx48X5HK50KNHDyE1NVUfr1QqBT8/P8HT01NISEjIzS6IiFhFjx49BA8PD2HXrl36uODgYAEQwsLChJcvX9q9T7k2Z509ezZjx45lwIABzJs3L8NmvYuLC2FhYXh5eVGwYMHc6oKIiFXcunWLa9euUadOHf3tmIB+68ZRroi5ItZHjx4xceJEKlasyKhRo7JsJkskEsqVK0dUVFRuNC8ikiOuXLlCbGws5cuXz7C3evHiRQDq1atH/vz57d6vXBHr8uXLiYuL47vvvsPDw8NgnqJFi+Lr65sbzYuI5Ig7d+7w8OFDatasSdGiRQGIioriyJEjjB071mE3/ufKAlN0dDRqtZr69eub/boMERFn4fbt2wCsWbOGs2fPEhcXR8mSJVm4cCH/+9//jA5AuY3NlaRSqXj48CEA1atXN3ilpoiIs/Ls2TMuX75M2bJl+frrryldujRSqZRDhw6xdOlS/a2a5vi42xqbizUxMVE/AX+TXl0g8nZw8+ZNLl++zEcffUTv3r0pXrw48PqKoQEDBvDy5UsWLVpE+fLl7d43mw97Xl5eetP3xo0bBk9TKJVKunfvztOnT23dvIhIjrhy5QoXLlzg3Xff1QsV4N1336VkyZLs37+fJ0+eOKRvuWKj6u7zjY6OznKAV6vVsmnTJkqVKmX07W0iIo7i0qVLSKVSqlWrliH+999/JzY2lgYNGugXnexNroh1+vTpVKxYkZkzZzJjxgz9Kwa1Wi1+fn5cv36dYcOGOfx8oIhIeu7cucPZs2fx9PTMsP+/ZMkSoqKicHNzY9iwYfq3Edqd3PK2uH79utChQwdBLpcLlSpVEqpUqSL4+PgI0dHRwqNHj3KrWRERi3n16pUwYcIEoWDBgoJMJhMAwcvLS6hatapQrVo1QSaTCV26dBH++eefDJ549iZXz7PGxcXx4MGDDA78derUeesPQos4F1qtlnv37vHo0SO9p51Go8ngqZTZQcIRiIfPRUTyCOImqIhIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHkEUq4hIHuH/ATHaVqGuLK7PAAAAAElFTkSuQmCC)
physics-General
physics-
A ray of monochromatic light is incident on one refracting face of a prism of angle
. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is
, the angle of incidence on the first face of the prism is
![](data:image/png;base64,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)
A ray of monochromatic light is incident on one refracting face of a prism of angle
. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is
, the angle of incidence on the first face of the prism is
![](data:image/png;base64,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)
physics-General
physics-
A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will
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Nzc5PTp09TVVWFzWbDYDA8dWdaCMHKygp3797dOocqGWZ9d4JGoyEvLw+TyUR/fz+HDh0iOzs74Ub4kiIc4XAYr9dLT08PXV1drK2tUVxcTF1dHY2NjWRnZ6PT6X7QXy+/38/Y2Bj9/f28+eab5OTkxPBfkFyEEGRnZ1NbW8vVq1c5f/48NpvtWwc84llChyMcDrO6uorH42FgYID+/n7S0tI4cuQIR44cea5TBz0eD11dXVtDksl8cEIspKWlYTKZyMnJ4ebNmxQXF8tw7ARFUVhfX2dlZYXOzk76+voQQlBbW8u5c+ee+06MYDDIwMAAPT09/P73vyc7OzuK1e8OoVCIjIwMTpw4wV/+8hdefPFFDAZDQo1cJU6l/xEOh9nY2OBvf/sbHR0dGAwGWlpaOH36NCUlJVF5r/V4PIyOjmKxWKivr5d9jWek0+nIy8vDaDTS2dmJyWSiqKhI7bKeWsKEQ1EUlpeX6e7u5p///Cc+n48LFy7Q0tKCxWIhMzMzKsEQQnDv3j2mp6d59913SUlJSciRlngQWZT44x//mH/9619UVVVRWFiYMD/PuA6HEAJFUXj06BHDw8O0t7ezvLzM0aNH2bdvHzU1NeTl5UW1qX7w4AGTk5OUlZVRU1OTML/IeCSEQKPRkJ+fT15eHmNjY9hsNgoLC9Uu7anEbTiCwSCPHz/G6XTS09OD2+2mpKSEl19+mYMHD5KXlxf11x1FUbDb7SwuLnLx4kXZ14gSnU7HkSNHcDqdW5OCiTCsG1fhiLQUkREoh8PBnTt3yMjI4NixYxw6dChmK2IVRWFtbQ273U5paSn79u1LiF9gIojMmrtcLvr6+qioqMBoNKpd1veKm3BEJvBWVla4du0aX331FVlZWVy8eJH9+/dTVFQU09Ww4XCYqakpPB4Ply5dIj8/P2bP2m0URSErK4vi4mIcDgeHDx8mJycn7l9Z4yIc4XCY9fV12trati5GuXDhAufPn98a/ov1D9Lr9fLFF19QXl5OVVWVXJYeZZFZ8+npae7fv781KRjPAYlJOIQQW7vsIlfzKoqCoihb/x2+7lesr6/jdru5d+8eDx484OTJkzQ2NlJeXr5jBzOHQiEePnxIR0cHv/71rxN2oVw8E0JQVFTE3r176e7u5sKFCxQWFsb1MHnMWg6/38/S0hKzs7MsLi6ytLTExsbG1majcDiMz+cjEAigKApVVVUcPXr0vzYc7ZSHDx/S1taG1WrFZrORnp6+Y8/eTdLS0sjPzyctLY22tjYuXbr0jR2X8SQm4dBoNGi1WjY2NpiZmcFut+NwOJicnGRhYYFgMEhKSgolJSW0trby0ksvUV9fr8qRLoFAgImJCdrb2/nFL36xK64RUIuiKBiNRmpra2lra+PMmTOkpaXF7ax5zKpKS0ujvLycwsJCmpqasNvtfPDBB/T29uLz+di7dy8//elPef3117Farao1r0tLSzgcDnJycmhpaYnrv2SJLnKvYF5eHuFwmI6ODs6cOYPJZFK7tG8Vsz+RGo1may92f38/77//Pjdu3ABAr9fzs5/9jDfffJPy8nLVghHZAut0OnnjjTfIyMiQfY0YE0KQk5PDiy++yOeff87Dhw/j9vKbmLUcm5ubjI2N8ec//xm73Y7RaOTixYsMDAyQn5/Pm2++qXrHd35+nqGhIYxGI83NzXHbvCeblJQUcnNz0Wq1OJ1OLBYLubm5apf1DVH9NAghCIVCTE9P43A46OzsxOfz8dprr9HU1MTMzAxer5e33noLm82m6jJwRVEYHx/H4/HQ0tKSEOPuyUKj0ZCTk0NdXR0Oh4Pa2lpycnLirq8XlXBEQrGyssLIyMjWsGxFRQWvvfYalZWVWzPf586d4+TJk2RlZan2YYwcED0wMEB6ero8EFoFOp2OPXv20NnZidPpxGq1xl1/77k+EZFQbGxsMDk5SW9vL93d3eh0Os6ePcsLL7yAyWRCo9GwvLyMxWLh0KFDqs8+K4qCx+PB5XLR2tqaUMuok4UQApPJRH5+Pg6Hg8bGxri7zuGZwxFZ7jE7O0tfXx9ffvkla2trvP3225w6deob20qzs7OpqamJizmEUCjErVu3SE9PZ9++fXKBoQqEEKSlpZGbm8vY2Bi9vb1xd7fHM4VDCIHH4+HmzZt0dXURDAZpbW3l1KlTFBQUfGtfIjU1FaPRqPpfhsjW2ra2Nt5+++2EPnQs0YXDYSorK1lbW+P27ducPn16600jHjx1OCIz2/Pz89y4cYPZ2VkURaGpqYn6+nrKy8sxGo3bJl+j0cTFP/rRo0d88cUXmEwm9u3blxRH5SeqyLyH2WxmdnaW27dv86Mf/Shu1rU9VTiCwSCzs7NbM90LCwtUVVVx5MgRysrKMBgMCbF5PhQKMTMzw+XLl3nnnXfifm3PbhAOhykoKKC0tJRr165x4sQJcnNz4+L3sm04Ip1tr9fL+Pg47e3tjI+PYzAYuHDhAs3NzXE5/PZdHj9+jN1uRwjB4cOHE2JPQbITQpCVlYXZbGZgYIC+vj6OHTsWFy36N8IRWTXr8/nweDz09vZit9sJBAKcOHGCV155JSHPcFIUhampKXp7e3nnnXfIy8uLi9c86evfTeRm3s8//5zq6uq4uPzmG+EIBoO4XC7u3LlDT08P8PXeimPHjmEymRJ2PmB9fR2n00kwGOT06dNyqUic0ev1FBQU0N/fj8vlIi8vT/V5Dx38/2niS0tLXLlyhcHBQYxGI+fOnaO6uhqr1UpWVlZcvAc+K7fbjcPh4ODBg3I2PA5pNBrMZjOlpaXcu3ePiooK1ec9dJF9F+3t7YyNjaHVamlsbKS+vp6Kigqys7MT/ngav9/PwMAAAA0NDd+4nEaKD3q9nvLycoaHhxkfH6eoqEjVeTHd/fv36enpYXx8HKvVSmtrK/v378dgMCTNB2hxcZHOzk7q6+vlNQJxTAiB1WplbGyMvr4+6urq1A3H5cuXMRqNW8s9ku2VI3JIG0BlZWXc7h2Qvn61ys7OJj8/n6WlJYaHh1W961174sQJfvWrX/GTn/wkLmawoykyHP2Pf/yD+vp6Ghoa1C5J+g6RJUmHDh1CURTa2toIBoOq1aM9d+5cXK6ljwav18unn36K0Wikrq4uIYegd6PU1FRKSkoIhUJbrb4atJmZmQk9CrUdRVFYWVnhr3/9Ky0tLVRUVCTsMPRuoygKFRUVZGVlce3aNYLBoCq7BbXJ9Br1pPX19a3Z8MbGxrha0CZ9t8jlN2azmdXVVfr7+wkEAjteR+Ks/fgBFEVhaWmJu3fv8uKLL2K1WmWrkYCKi4vJzc3l6tWreL3erTPQdkpShsPv9zM6Osra2hqnT59OuDVg0tcjV5mZmVgsFjweD9PT0zveOU+6T4wQguXlZRwOBxaLhfLyctlqJCAhBCkpKVutfm9vL2traztaQ9KFQ1EUBgcHefz4MYcPH47apTbSztNoNOj1eiorK5mYmGBqampHW4+k+9Ssrq7S29uLwWCgrq5OBiOBRS6/sdlsrK2tMTIygtfr3bHnJ90np6enh7W1NaqrqykoKFC7HOk5aTQaDAYD+fn5TE5OMj4+vmPDukkTDiEEm5ubtLW1UVhYSENDQ1LO3+w2kRXjzc3NrKys0NPTg9/v35FnJ004gsEgHR0drK6uUltby549e9QuSYoSIQQGgwGDwYDb7cbpdO7Ic5MiHEIIvF4vn3zyCTU1NdTU1MhWI8mEQiEaGxvRaDR0dHQQCoVi/nqVFOHw+XwMDQ3x+PFj6urqKCgokLPhSSg7Oxuj0cjs7Cyjo6NblyDFSsKHQwjB6uoqnZ2d7Nu3j6qqqrg4OE6KPq1WS2lpKaFQiK6uLjY3N2PaeiR8OAKBwNbd4UePHlV1/b8UW5GRK6PRiMPhYG5ujlAoFLPnJfynaG1tjdHRUbKysqipqVH15HYptiKHwFVXV+P1enE4HGxsbMTseQkfjrGxMSYmJrZW3sqOeHKLrLnKz8+nv7+fhYWFmC1ITOhwrK+v09/fj6IoHDt2TK6h2gWEEOh0OpqampiamsLlcuHz+WLyrIQOh91uZ3Z2lsrKSkpKSmRfY5fQarXk5uZSVFTE0NAQ09PTsXlOTL5rjEUun7lz5w5paWkcPXpUthq7SOSe+6NHjzI5Ocnw8HBMZs0TNhwjIyM8ePCA0tJSKisr1S5JUoHJZEKv1+NyufB4PFH//gkZjmAwyOXLl7FYLLLV2MXC4TDHjh1jcXGRe/fuRX3OI+HC4ff7cblczM/PU1VVJfsau5zRaCQnJ4eZmRncbndUA5JQf3KFEGxsbHDnzh1MJhMHDhxQ/bBhtWk0GrRaLWlpaTFfThGPUlNTqaqqoru7m/7+fiwWS9Quv0mocIRCITweD/fv36euro5QKMTs7KzaZakmHA6zsbFBdnY2Op1uV75earVa8vLyALh79y7Nzc1Ru5QooX6awWCQiYkJBgcHt/aK78YPxJPcbjcZGRl8+umnu7Ll0Gg0+Hw+ZmZmWFhYwO12k5eXF5VwaIQap2U9o0h/48aNGwghUBRFlcO+4klaWtrWhqDdKvJqmZGRwdmzZykpKYnKq1VChSNy9u3m5qbapUhxSKvVotfro3ZlRkKFQ5J2khwDlaRtyHBI0jZkOCRpGzIckrQNGQ5J2oYMhyRtQ4ZDkrYhwyFJ25DhkKRtyHBI0jZkOCRpGzIckrQNGQ5J2oYMhyRtQ4ZDkrYhwyFJ25DhkKRtyHBI0jZkOCRpGzIckrQNGQ5J2oYMhyRtQ4ZDkrYhwyFJ25DhkKRtyHBI0jb+DyU5JpQ574ipAAAAAElFTkSuQmCC)
A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will
![](data:image/png;base64,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)
physics-General
physics-
A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is
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)
A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is
![](data:image/png;base64,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)
physics-General
physics-
A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is
A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is
physics-General
physics-
A small particle of mass
is projected at an angle
with the
-axis with an initial velocity
in the
-
plane as shown in the figure.
the angular momentum of the particle is
![](data:image/png;base64,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)
A small particle of mass
is projected at an angle
with the
-axis with an initial velocity
in the
-
plane as shown in the figure.
the angular momentum of the particle is
![](data:image/png;base64,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)
physics-General
physics-
The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is
![](data:image/png;base64,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)
The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is
![](data:image/png;base64,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)
physics-General
Maths-
If the normal at the point
to the ellipse
intersects it again at the point
, then
is
If the normal at the point
to the ellipse
intersects it again at the point
, then
is
Maths-General
physics-
A fighter plane enters inside the enemy territory, at time
with velocity
and moves horizontally with constant acceleration
(see figure). An enemy tank at the border, spot the plane and fire shots at an angle
with the horizontal and with velocity
. At what altitude
of the plane it can be hit by the shot?
![](data:image/png;base64,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)
A fighter plane enters inside the enemy territory, at time
with velocity
and moves horizontally with constant acceleration
(see figure). An enemy tank at the border, spot the plane and fire shots at an angle
with the horizontal and with velocity
. At what altitude
of the plane it can be hit by the shot?
![](data:image/png;base64,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)
physics-General
physics-
A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C</em
A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C</em
physics-General
physics-
A particle of mass
is rotating in a horizontal circle of radius
and is attached to a hanging mass
as shown in the figure. The speed of rotation required by the mass
keep
steady is
![](data:image/png;base64,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)
A particle of mass
is rotating in a horizontal circle of radius
and is attached to a hanging mass
as shown in the figure. The speed of rotation required by the mass
keep
steady is
![](data:image/png;base64,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)
physics-General
physics-
Figure shows the variation of the stopping potential (V0) with the frequency (v) of theincident radiations for two different photosensitive material M1 and M2 .What are the values of work functions for M1 and M2 respectively
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458522/1/937235/Picture73.png)
Figure shows the variation of the stopping potential (V0) with the frequency (v) of theincident radiations for two different photosensitive material M1 and M2 .What are the values of work functions for M1 and M2 respectively
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458522/1/937235/Picture73.png)
physics-General
physics-
The respective angles of the flint and crown glass prisms are
and A. They are to be used for dispersion without deviation, then the ratio of their angles
will be
The respective angles of the flint and crown glass prisms are
and A. They are to be used for dispersion without deviation, then the ratio of their angles
will be
physics-General