Question

A ray of light is incident on a prism whose refractive index is 1.52 at an angle of 40°. If the angle of emergence is 60°, calculate the angle of the prism. 

Answer 1

Given : 

`mu = 1.52`   `i = 40^circ`

`e = 60^circ`   A = ?

`mu = sin i/sin r`

`1.52 = sin 40^circ/sin r`

`therefore sin r = 0.6427/1.52`

`sin r = 0.4228`

`therefore r = sin^-1(0.4228)`

`r = 25.01^circ`

`1/mu = (sin r')/sin e ⇒ sin r' = sin e/mu`

⇒ `sin r' = sin 60^circ/1.52 = 0.866/1.52 = 0.57`

⇒ `r' = sin^-1(0.57) = 34.75^circ`

`therefore A = r + r' = 25.01^circ + 34.75^circ = 59.76^circ`