A prism of a certain angle deviates the red and blue rays by `8^@` and `12^@` respectively. Another prism of the same angle deviates the red and blue rays by `10^@` and `14^@` respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

Options

A. `5 : 6`
B. `9 : 11`
C. `6 : 5`
D. `11 : 9`

Answer

C

Explanation

For one prism,
`omega_(1) = (delta_(B) - delta_(R))/(delta) = (12-8)/(10)(therefore delta = (delta_(B) + delta_(R))/(2))`
or `omega_(1) = (4)/(10)`
For other prism, `omega_(2) = (delta_(B) - delta_(R))/(delta) = (14-10)/(12)(therefore delta = (14 + 2)/(2))`
`omega_(2) = (4)/(12) = (1/3)`
`therefore (omega_(1))/(omega_(2)) = (4 xx 3)/(10 xx 1)` or `(omega_(1))/(omega_(2)) = 12/10 = 6/5`