Question

One method of determining the refractive index of a transparent solid is to measure the critical angle when the solid is in air. If `θ_c` is found to be 40.7°, what is the index of refraction of the solid?

Answer 1

The citical angle `theta_c` of a medium denser than air is the angle of incident of a ray in that medium refracted in air for which the angle of refraction becomes `90^@`

So refractive index `mu` of the medium w.r to air will be

`mu=sin("Angle in rarer medium")/(sin("Angle in the deser medium"`
`=(sin90/sintheta_c) =(1/sin40.7^@)~~1.53`