Question

Calculate the critical angle for diamond having a refractive index of 2.42 and Crown glass having a refractive index of 1.52.

Answer 1

Hint:Critical angle is the angle at and beyond which light starts to reflect instead of refract when it is incident from one media towards the surface of the second media. Light cannot reflect if the angle is lower than the critical angle. Here, assuming the first medium being air, use Snell's law to find the critical angle.

Complete step by step solution:
When a ray of light passes from one medium to the other, it refracts. Critical angle is the angle at which when a ray of light is incident on a surface of a different medium, instead of refracting, the light reflects from the surface. This phenomenon is known as total internal reflection.

Here, we assume that the light is travelling from air to diamond or crown glass. We will use Snell's law to find critical angles. The refractive index of air is 1, the critical angle for diamond would be as follows:

\[{n_{(air)}}\sin {\theta _{(air)}} = {n_d}\sin C\]
Here, n air is the refractive index of air, \[\sin {\theta _{(air)}}\]is the angle of incidence, n d is the refractive index of diamond and sinC is the critical angle.
\[ 1\centerdot 1=2.42\sin C \\
\sin C=\dfrac{1}{2.42} \\
C=24.4{}^\circ \\
\].
Thus, the critical angle for diamond is\[24.4^\circ \].
For the case of crown glass;
\[{n_{(air)}}\sin {\theta _{(air)}} = {n_c}\sin C\]
Where n c is the refractive index of crown glass and sinC is its critical angle.
\[
1\centerdot 1=1.52\sin C \\
\sin C=\dfrac{1}{1.52} \\
C=41.14{}^\circ \\
\]

Thus, the critical angle for crown glass is 41.14 degree.

Notes:Total internal reflection can only occur when the ray of light passes from a rarer medium to a denser medium. In reality, there is an extreme amount of total internal reflection in diamond as well as crown glass, and because of this phenomenon, diamond shines the most. It is because of its high refractive index that is less critical.