Define critical angle for a given pair of medium and find the relation between critical angle and refractive index.

Explanation

Critical angle for a pair of media in contact is the angle of incidence in the denser medium for which the angle of refraction is `90^(@)` in the rarer medium.
Relation between critical angle and refractive index
Let C be critical angle for any two media 1 and 2. Let media 2 be denser than media 1. Since at critical angle, the angle of refraction is `90^(@)`.
i.e. when i = C, `r = 90^(@)`
`:.` From Snell.s law, we have
`(sin C)/(sin 90^(@))=""^(2)mu_(1)` or `""^(1)mu_(2)=(1)/(sin C)`
If medium 1 is air having refractive index 1 and the denser medium 2 has refractive index `mu` then the above equation becomes
`mu=(1)/(sin C)`