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  4. In the figure, a ray of light is perpendicular to the face AB of a glass prism (μ=1.52). Find the value of θ so that the ray is totally reflected at face A C, if the prism is immersed in water (μ=1.33). Given sin 61°=0.875

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Q. In the figure, a ray of light is perpendicular to the face $AB$ of a glass prism $(\mu=1.52)$. Find the value of $\theta$ so that the ray is totally reflected at face $A C$, if the prism is immersed in water $(\mu=1.33)$. Given $\sin 61^{\circ}=0.875$Physics Question Image

AIIMSAIIMS 2018Ray Optics and Optical Instruments

Solution:

Given, $\mu_{ g }=1.52, \mu_{ w }=1.33, \theta=?$
Apply Snell's law at point D,
$\mu_{ g } \sin i _{ C}=\mu w \sin 90^{\circ}$
$\Rightarrow \sin i_{c}=\frac{\mu_{w}}{\mu_{g}}=\frac{1.33}{1.52}$
$\Rightarrow i_{c}=\sin ^{-1}\left(\frac{1.33}{1.52}\right)=61^{\circ}$
From figure, $\theta+i_{c}=90^{\circ}$
$\Rightarrow \theta=90^{\circ}-61^{\circ}=29^{\circ} \approx 30^{\circ}$

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