SATHEE: Optics 4 Question 16

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:

Let $δ_{m}$ be the angle of minimum deviation. Then

$\begin{aligned} μ & = \frac{\sin \frac{A + δ_{m}}{2}}{\sin (A / 2)} (A = 60^{\circ} for an equilateral prism) \\ ∴ \sqrt{2} & = \frac{\sin \frac{60^{\circ} + δ_{m}}{2}}{\sin \frac{60^{\circ}}{2}} \end{aligned}$

Solving this we get $δ_{m} = 30^{\circ}$

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

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

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Optics 4 Question 16

17. A ray of light undergoes deviation of 30∘ when incident on an equilateral prism of

Answer:

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