SATHEE: ray-optics-and-optical-instruments Question 17

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Question: Q. 2. A ray of light incident at an angle $θ$ on a refracting face of a prism emerges from the other face normally. If the angle of the prism is $5^{\circ}$ and the prism is made of a material of refractive index 1.5, the angle of incidence is : (a) ${7.5}^{\circ}$ . (b) $5^{\circ}$ . (c) $15^{\circ}$ . (d) ${2.5}^{\circ}$ .

[NCERT Exemplar]

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Solution:

Ans. Correct option : (a)

Explanation : Given that,

$\begin{aligned} A & = 5^{\circ} μ & = 1.5 i_{2} & = 0^{\circ} r_{2} & = 0^{\circ} \end{aligned}$

As we know that,

$\begin{aligned} r_{1} + r_{2} & = A r_{1} & = A - r_{2} & = 5 - 0 = 5^{\circ} \end{aligned}$

From Snell’s law :

$\begin{aligned} μ & = \frac{\sin i_{1}}{\sin r_{1}} \sin i_{1} & = μ \sin r_{1} & = 1.5 \times \sin 5^{\circ} & = 1.5 \times 0.087 & = 0.1305 & = {7.5}^{\circ} \end{aligned}$

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