Optics Ques 3
- For an isosceles prism of angle $A$ and refractive index $\mu$, it is found that the angle of minimum deviation $\delta_m=A$. Which of the following options is/are correct?
(2017 Adv.)
(a) For the angle of incidence $i_1=A$, the ray inside the prism is parallel to the base of the prism
(b) At minimum deviation, the incident angle $i_1$ and the refracting angle $r_1$ at the first refracting surface are related by $r_1=\left(\frac{i_i}{2}\right)$
(c) For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is $i_1=\sin ^{-1}\left[\sin A \sqrt{4 \cos ^2 \frac{A}{2}-1}-\cos A\right]$
(d) For this prism, the refractive index $\mu$ and the angle prism $A$ are related as $A=\frac{1}{2} \cos ^{-1}\left(\frac{\mu}{2}\right)$
Show Answer
Answer:
Correct Answer: 3.( a, b, c )
Solution:
Formula:
For this prism when the emergent ray at the second surface is tangential to the surface
$ \begin{aligned} & i_2=\pi / 2 \Rightarrow r_2=\theta_c \Rightarrow r_1=A-\theta_c \\ & \text { so, } \sin i_1=\mu \sin \left(A-\theta_c\right) \end{aligned} $
so,
$ i_1=\sin ^{-1}\left[\sin A \sqrt{4 \cos ^2 \frac{A}{2}-1}-\cos A\right] $
For minimum deviation through isosceles prism, the ray inside the prism is parallel to the base of the prism if $\angle B=\angle C$.
But it is not necessarily parallel to the base if,
$ \angle A=\angle B \text { or } \angle A=\angle C $
BETA
