If the critical angle for total internal reflection from a medium to vacuum is 30^∘. Then the speed of light in the medium is

CONCEPT:

Total internal reflection (TIR):

• Total internal reflection (TIR) occurs at the interface of two transparent medium when the ray of light travels from a denser medium to a rarer medium.
• The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.
• Total internal reflection (TIR) of light is the reflection of light within the same medium when a ray of light is incident at the interface of two medium at an angle of incidence which is greater than the critical angle for the pair of media i.e. i > ic.
• The relation between refractive index and critical angle is

\(μ =\frac{1}{\sin C}\)

CALCULATION:

Given  - critical angle (C) = 30∘

• The relation between refractive index and critical angle is

\(\Rightarrow \mu =\frac{1}{\sin C}\)

\(\Rightarrow \mu =\frac{1}{\sin 30}=2\)

As we know, the refractive index is written as

\(\Rightarrow \mu=\frac{c}{v}\)

\(\Rightarrow v = \frac{3\times 10^8}{2}=1.5\times 10^8\, m/s\)