A thin prism P with angle `4^(@)` and made from glass of refractive index 1.54 is combined with another thin prism P made from glass of refractive index 1.72 to produce dispersion without deviation The angle of prism P is

Options

A. `4^(@)`
B. `5.33^(@)`
C. `2.6^(@)`
D. `3^(@)`

Answer

D

Explanation

Angle of deviation `delta=(n-1)A`
Dispersion produced by both the prism will be equal
`(n_(1)-1)A_(1)=(n_(2)-1)A_(2)`
`A_(2)=((n_(1)-1)A_(1))/((n_(2)-1))=((1.54-1)xx4)/((1.72-1))=3^(@)`
Hence, the angle of prism `P_(2)` is `=3^(@)`