A ray of light is incident normally on one of the faces of a prism of apex angle 30 degree and refractive index sqrt2. The angle of deviation of the ray is…degrees.

Options

A. `12.5^(@)`
B. `22.5^(@)`
C. `10^(@)`
D. `15^(@)`

Answer

D

Explanation

For the prism `A = 30^(@) , n = sqrt2`
When the ray of light is incident normally i= 0 , `r_(1) = 0`

But in a prism , `r_(1) + r_(2) = A`
`therefore r_(2) = A - r_(1) but r_(1) = 0 , r_(2) = A = 30^(@)`
But `n = (sin e)/(sin r_(2)) therefore sin e= n sin r_(2) sin e = sqrt2 xx sin 30^(@) = (1)/(sqrt2) therefore e = 45^(@)`
For a prism , `A + delta = i+ e therefore delta i + e - A `
`therefore delta = 0 + 45^(@) - 30^(@) = 15^(@)`