ray-optics-and-optical-instruments Question 17
Question: Q. 2. A ray of light incident at an angle $\theta$ 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,
$$ \begin{aligned} A & =5^{\circ} \ \mu & =1.5 \ i_{2} & =0^{\circ} \ r_{2} & =0^{\circ} \end{aligned} $$
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 :
$$ \begin{aligned} \mu & =\frac{\sin i_{1}}{\sin r_{1}} \ \sin i_{1} & =\mu \sin r_{1} \ & =1.5 \times \sin 5^{\circ} \ & =1.5 \times 0.087 \ & =0.1305 \ & =7.5^{\circ} \end{aligned} $$
