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^(@)`

Answer

D

Explanation

(d) 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)rArr(mu_(1)-1)A_(1)=(mu_(2)-1)A_(2)`
`rArr A_(2)=((mu_(1)-1))/((mu_(2)-1))A_(1)`
Given, `mu_(1)=1.54,A_(1)=4^(@),mu_(2)=1.72`
`rArrA_(2)=((1.54-1))/((1.72-1))xx4=3^(@)`