Question

the critical angle of glass is 42° and that of water is 49°.A galss prism is imersed in water .then the critical angle for total internal reflection in the prism imersed in water is​

Answer 1

Answer:

62°

Explanation:

Let

The refractive index of the prism glass be $n_g$ and the refractive index of the water be $n_w$

Given

Critical angle of glass $=42^\circ$

Therefore,

from Snell's law

$\frac{1}{n_g}=\sin 42^\circ$

Similarly given that crictical angle of water is $49^\circ$

Therefore,

$\frac{1}{n_w}=\sin 49^\circ$

If the glass prism is immersed in water then critical angle will be formed when the light ray enters from denser (glass) medium to rarer (water) medium

Therefore, from Snell's law again

$\frac{n_w}{n_g}=\frac{\sin i}{\sin 90^\circ}$

$\implies \frac{\sin42^\circ}{\sin 49^\circ}=\frac{\sin i}{1}$

$\implies \sin i=\frac{0.669}{0.755}$

$\implies \sin i=0.886$

$\implies i=\sin^{-1}0.886$

$\implies i=62.37^\circ$

Hope this helps.