Optics 4 Question 16

17. A ray of light undergoes deviation of $30^{\circ}$ when incident on an equilateral prism of

refractive index $\sqrt{2}$. The angle made by the ray inside the prism with the base of the prism is …..

(1992, 1M)

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Answer:

Correct Answer: 17. $30^{\circ}$

Solution:

  1. Let $\delta _m$ be the angle of minimum deviation. Then

$$ \begin{aligned} \mu & =\frac{\sin \frac{A+\delta _m}{2}}{\sin (A / 2)}\left(A=60^{\circ} \text { for an equilateral prism }\right) \\ \therefore \sqrt{2} & =\frac{\sin \frac{60^{\circ}+\delta _m}{2}}{\sin \frac{60^{\circ}}{2}} \end{aligned} $$

Solving this we get $\delta _m=30^{\circ}$

The given deviation is also $30^{\circ}$ (i.e. $\delta _m$ )

Under minimum deviation, the ray inside the prism is parallel to base for an equilateral prism.



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