Question

Arrange the following combinations in the increasing order of critical angle:
a) Air, water interface
b) Air, glass interface
c) Water, glass interface
d) Air, diamond interface

• A. d, b, a, c
• B. a, b, c, d
• C. d, c, b, a
• D. b, c, a, d

Answer 1

The correct option is A d, b, a, c

${\mu }_{air}=1$

${\mu }_{water}=1.33$

${\mu }_{glass}=1.5$

${\mu }_{diamond}=2.$

Critical angle, sin ${\theta }_c=\frac{{\mu }_1}{{\mu }_2}$

where ${\mu }_1$ is refractive index of rarer medium.
and ${\mu }_2$ is refractive index of denser medium

So, for air and water ${\theta }_{c_1}=si{n}^{-1}\left(\frac{1}{1.33}\right)$$={48.75}^0$

for air and glass ${\theta }_{c_2}=si{n}^{-1}\left(\frac{1}{1.5}\right)={41.81}^0$

for water and glass ${\theta }_{c_3}=si{n}^{-1}\left(\frac{1.33}{1.5}\right)={62.45}^0$

for air and diamond ${\theta }_{c_4}=si{n}^{-1}\left(\frac{1}{2}\right)={30}^0$

So, clearly ${\theta }_{c_4}<{\theta }_{c_2}<{\theta }_{c_1}<{\theta }_{c_3}.$

So, correct order is $d<b<a<c$