A ray of light undergoes total internal reflection while moving from a denser to a rarer medium Derive - Science - The Human Eye and the Colourful World

Question

A ray of light undergoes total internal reflection while moving
from a denser to a rarer medium Derive the relation connecting
critical angle and refractive indices of the two media

Kranav Sharma · Accepted Answer

* Total internal reflection is the phenomenon of reflection of light into a denser medium from an interface of the denser medium and the rarer medium.

* Two essential conditions for total internal reflection:

Incident ray should travel in denser medium and refracted ray should travel in rarer medium.

Angle of incidence (i) should be greater than the critical angle for the pair of media in contact.

Relation between refractive index (μ) and critical angle (C)

When, i = c, r = 90°; Applying Snell’s law at A₂, we get

μ_b sin c = μ_b sin 90° = μ_a× 1

Relation between refractive index (Î¼) and critical angle (C) When, i = c, r = 90Â°; Applying Snellâ€™s law at A2, we get Î¼b sin c = Î¼b sin 90Â° = Î¼a Ã— 1

A ray of light undergoes total internal reflection while moving from a denser to a rarer medium . Derive the relation connecting critical angle and refractive indices of the two media .