Question

A transparent solid cylindrical rod (refractive index `2/sqrt 3`) is kept in air. A ray of light incident on its face travels along the surface of the rod, as shown in figure. Calculate the angle θ.

Answer 1

Using TIR formula:

sin i_c = `1/mu_"cylinder"`

sin i_c = `sqrt 3/2`

sin i_c = sin 60°

⇒ i_c = 60°

Using snell’s law of refraction,

`(sin theta)/(sin 30^circ) = 2/sqrt 3`

sin θ = `2/sqrt 3 xx 1/2`

θ = `sin^-1(1/sqrt3)`