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Ray Optics

Section: Physics

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Question : 3 of 17

Marks: +1, -0

A light ray falls on a rectangular glass slab as shown in the figure. If total internal reflection occurs at the vertical face of the slab at point

B

, the refractive index of glass is

[AP EAPCET 23 May 2025 S1]

$\sqrt{\;\frac{3}{2}}$
$\;\frac{(\sqrt{3+1})}{2}$
$\;\frac{(\sqrt{2+1})}{2}$
$\;\frac{\sqrt{5}}{2}$

Solution:

For surface

X Y

,

\;\mu_a \sin 45^{\circ} = \mu g \sin \; r_1

\;\mu_g \sin \;r_1 = \;\frac{1}{\sqrt{2}}

\;\Rightarrow \;\; \sin \;r_1 = \;\frac{1}{\mu_g \sqrt{2}} \;\;\;\cdot\cdot\cdot\cdot\cdot\cdot\cdot (i)

∴ From figure,

i_2 = 90 - r_1

For total internal reflection

\;\sin \;i_2 = \;\frac{1}{\mu_g}

\Rightarrow \sin \; (90-r_1) = \;\frac{1}{\mu_g} \;\;\;\cdot\cdot\cdot\cdot\cdot\cdot\cdot (ii)

\Rightarrow \cos r_1 = \;\frac{1}{\mu_g}

From eqn. (i) and (ii),

\sin^2 r_1 + \cos^2 r_1 = 1

\Rightarrow \;\frac{1}{2 \mu_g^2} + \;\frac{1}{\mu_g^2} = 1 \Rightarrow \;\frac{3}{2 \mu_g^2} = 1

\Rightarrow \mu_g^2 = \;\frac{3}{2} ; \therefore \mu_g = \sqrt{\;\frac{3}{2}}

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