In a direct vision spectrograph , there are 3 crown glass prisms and 2 flint glass prisms , each of refracting angle `24^(@)` . What should be the angle of the crown glass prism , if the refractive index of crown glass for mean colour is `1.52` and that of flint-glass of 1.65 ?

Options

A. `18^(@)`
B. `20^(@)`
C. `22^(@)`
D. `25^(@)`

Answer

B

Explanation

In a direct vision prism, we get dispersion without deviation . For this ,
`3 A (n_(y) - 1) = 2 A' (n'_(y) - 1)`
`therefore 3 A (1.52 - 1) = 2 xx 24 (1.65 - 1)`
`therefore 3 A xx 0.52 = 48 (0.65)`
`therefore A = (48)/(3) xx (0.65)/(0.52) = 16 xx (5)/(4) = 20^(@)`