What is the maximum value of the refractive i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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?

Similar Questions

$A$ certain prism is found to produce a minimum deviation of $38^{\circ}$. It produces a deviation of $44^{\circ}$ when the angle of incidence is either $42^{\circ}$ or $62^{\circ}$. What is the angle of incidence when it is undergoing minimum deviation (in $^{\circ}$)?

The graph between the angle of deviation $(\delta)$ and the angle of incidence $(i)$ for a triangular prism can be represented by:

Find the value of the angle of emergence from the prism. The refractive index of the glass is $\sqrt{3}$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module