Critical Angle and Refractive Index

Derive the formula for relation between the Critical Angle and Refractive Index ?

Sol:

$Relation between the Critical Angle and Refractive Index$

Consider a ray of light AB, traveling in an optically denser medium, such that angle of refraction in optically rarer medium is 90°. In such a case ∠ABM is the critical angle.

As rays of light are traveling from medium 'b' to medium 'a'.

∴ ^bμ_a	=	sin i/sin r
or ^bμ_a	=	sin C / sin 90
∴ 1/^bμ_a	=	sin C / sin 90
∴ ^aμ_b	=	sin 90/ sin C [∵ 1/^bμ_a = ^aμ_b]
^aμ_b	=	1.0000 / sin C
^aμ_b	=	1/ sin C

From the above relation we can find critical angle of a material if its refractive index is known.