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

Explanation

For a thin prism, angle of minimum deviation is given by, `delta=(mu-1)A`
where, `mu` is refractive index of the prism and A is the angle of prism
For dispersion without deviation,
`delta_(1)=delta_(2)`
`implies (mu_(1)-1)A_(1)=(mu_(2)-1)A_(2)`
`implies A_(2)=((mu_(1)-1))/((mu_(2)-1))A_(1)`
Given, `mu_(1)=1.54, A_(1)=4^(@), mu_(2)=1.72`
`implies A_(2)=((1.54-1))/((1.72-1))xx4=3^(@)`