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Light is incident normally on face AB of a prism as shown in Figure. A liquid of refractive index $μ$ is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limit of $μ$ for which total internal reflection takes place at face AC is

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$μ \geq \frac{3}{4}$

$μ < \frac{3 \sqrt{3}}{4}$

$μ > \sqrt{3}$

$μ < \frac{\sqrt{3}}{2}$

answer is B.

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Detailed Solution

Critical angle between glass and liquid face:

$\sin θ_{c} = \frac{μ_{r}}{μ_{d}} = \frac{μ}{3 / 2} = \frac{2 μ}{3}$
Angle of incidence at face AC is $60^{0}$
i.e., $i = 60^{0}$
For total internal reflection to take place, $i > θ_{c}$

or, $\sin i > \sin θ_{c}$
or, $\sin 60^{0} > \frac{2 μ}{3}$

or, $μ < \frac{3 \sqrt{3}}{4}$

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