A monochromatic ray of light is incident normally on one of the refracting surfaces of a prism . The emergent ray grazes the second refracting surface . What is the angle of the prism if the refractive index of the material of the prism is `1.6` ?

Options

A. `35^(@)`
B. `39^(@)`
C. `42^(@)`
D. `44^(@)`

Answer

B

Explanation

In this case ,i= 0 , `r_(1) = 0` as the ray is incident normally on the first surface .
The emergent ray grazes the second refracting surface i.e. it goes parallel to that surface hence the angle of emergence `e = 90^(@)`
But for a prism `A = r_(1) + r_(2) = r_(2) " " because r_(1) = 0`
Using the formula , `n = (sin i)/(sin r)` for the second refracting surface , we have `n = 1.6 , i= 90^(@) and r =r _(2)`
`therefore 1.6 = (sin 90^(@))/(sin r_(2)) therefore sin r_(2) = (1)/(1.6) = (5)/(8) = 0.625`
`therefore r_(2) = sin^(-1) (0.625) = 38.68^(@) = A`
`therefore A = 38. 68^(@) = 39^(@)`