Question

The critical angle for refraction from glass to air is ${42}^{\circ }$ and that from water to air is ${48}^{\circ }$. Find the critical angle for refraction from glass to water.

• A. ${61}^{\circ }$3'
• B. ${51}^{\circ }$3'
• C. ${61}^{\circ }$2
• D. ${63}^{\circ }$3'

Answer 1

The correct option is D ${63}^{\circ }$3'

Given,

The critical angle for reflection from glass is $C_g={42}^{\circ }$

The critical angle of reflection for water$C_w={48}^{\circ }$

Now the refractive index of glass can be given as

${\mu }_g=\frac{1}{\sin C_g}=\frac{1}{\sin \left({42}^{\circ }\right)}=1.5$

Similarly, the refractive index of water is given as

${\mu }_w=\frac{1}{\sin C_w}=\frac{1}{\sin \left({48}^{\circ }\right)}=1.34$

Hence the refractive index of glass with respect to water is

$\mu =\frac{{\mu }_g}{{\mu }_w}=\frac{1.5}{1.34}=1.119$

Now the critical angle of glass with respect to water is given as

$\mu =\frac{1}{\sin C}\Rightarrow \sin C=\frac{1}{\mu }$

$C={\sin }^{-1}\left(\frac{1}{1.119}\right)={63}^{\circ }{3}^{\prime }$