Light is incident normally on the face AB of a prism as shown in the figure. A layer of liquid of refractive index μ is applied on the face AC of the prism. If the prism is made of glass of refractive

Question

Light is incident normally on the face AB of a prism as shown in the figure. A layer of liquid of refractive index μ is applied on the face AC of the prism. If the prism is made of glass of refractive index 3 2 , then the limit of μ for which total internal reflection takes place on face AC is

TestHub · Accepted Answer

For critical angle at the glass-liquid interface we have

$μ_{1} s i n C = μ_{2} s i n 90 °$

$\Rightarrow \frac{3}{2} s i n C = μ$

$\Rightarrow s i n C = \frac{2 μ}{3}$

For total internal reflection

$60 ° > C$

$\Rightarrow s i n 60 ° > s i n C$

$\Rightarrow \frac{\sqrt{3}}{2} > \frac{2 μ}{3}$

$μ < \frac{3 \sqrt{3}}{4}$

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