Ray Optics

JEE Main level, single correct, medium

258 of 295

Question 258 of 295

A prism of refractive index μ\mu and angle of prism AA is placed in the position of minimum angle of deviation. If minimum angle of deviation is also AA, then in terms of refractive,

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Answer: (A) 2cos⁡−1(μ2)2{\cos }^{-1}\left(\dfrac{\mu }{2}\right)

μ=sin⁡(A+δmin⁡2)sin⁡(A2)\mu =\dfrac{\sin \left(\dfrac{A+{\delta }_{\min }}{2}\right)}{\sin \left(\dfrac{A}{2}\right)}
μ=sin⁡(A+A2)sin⁡(A2)\mu =\dfrac{\sin \left(\dfrac{A+A}{2}\right)}{\sin \left(\dfrac{A}{2}\right)}
μ=sin⁡Asin⁡A2=2cos⁡A2\mu =\dfrac{\sin A}{\sin \dfrac{A}{2}}=2\cos \dfrac{A}{2}
A=2cos⁡−1(μ2)A=2{\cos }^{-1}\left(\dfrac{\mu }{2}\right)

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