Ray Optics and Optical Instruments - Result Question 14
14. A light ray falls on a rectangular glass slab as shown. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is
[2002]
(a) $\sqrt{3 / 2}$
(b) $\frac{(\sqrt{3}+1)}{2}$
(c) $\frac{(\sqrt{2}+1)}{2}$
(d) $\sqrt{5} / 2$
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Answer:
Correct Answer: 14. (a)
Solution:
- (a) For point A, $ _{a} \mu_g=\frac{\sin 45^{\circ}}{\sin r}$
$\Rightarrow \sin r=\frac{1}{\sqrt{2} _{a} \mu_g}$
For point $B, \sin (90^{\circ}-r)= _{g} \mu_a$ where, $(90^{\circ}-r)$ is critical angle.
$ \begin{aligned} & \Rightarrow _{a} \mu_g{ }^{2}=\frac{1}{1-\frac{1}{2_a \mu_g^{2}}}=\frac{2 _{a} \mu_g^{2}}{2 _{a} \mu_g^{2}-1} \\ & \quad \Rightarrow 2 _{a} \mu_g^{2}-1=2 \Rightarrow _{a} \mu_g=\sqrt{\frac{3}{2}} \end{aligned} $
