What is the maximum value of the refractive i | vedclass

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(D) For light to pass through a prism,the angle of incidence $i$ must be real. The condition for emergence is that the angle of refraction at the seco

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$\sqrt{1 + \cot^2(A/2)}$

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(D) For light to pass through a prism,the angle of incidence $i$ must be real. The condition for emergence is that the angle of refraction at the second surface $r_2$ must be less than or equal to the critical angle $C$. Given $r_1 + r_2 = A$,for emergence,$r_2 \leq C$. Since $r_1 \geq 0$,we have $r_2 = A - r_1 \leq A$. Thus,we require $C \geq r_2$. For the light to pass through for any angle of incidence,we must have $\sin C \geq \sin(A)$ (if $A However,the question asks for the condition where light *can* pass through. The limiting case is $\mu \sin(A/2) = 1$,which implies $\mu = \csc(A/2)$. Using the identity $\csc^2(A/2) = 1 + \cot^2(A/2)$,we get $\mu = \sqrt{1 + \cot^2(A/2)}$.

What is the maximum value of the refractive index of the material of a prism with prism angle $A$ such that light can pass through it?

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