The minimum deviations suffered by red, yellow and violet beam passing through an equilateral transparent prism are `38.4^(@), 38.7^(@)` and `39.2^(@)` respectively. Calculate the dispersive power of the medium.

Answer

`0.018`

Explanation

As the prism is equilateral, `:. A = (180)/(3) = 60^(@)`
`(delta_(m))_(r) = 38.7^(@), (delta_(m))_(v) = 39.2^(@)`,
`:. mu_(r ) = (sin(A + delta_(m))/(2))/(sin A//2) = (sin(60^(@) + 38.4^(@))/(2))/(sin 30^(@))`
`= (sin 49.2^(@))/(1//2) = 1.514`
`mu_( y) = (sin(60^(@) + 38.7^(@))/(2))/(sin 30^(@)) = (sin 49.35^(@))/(1//2) = 1.5184`
`mu_(v) = (sin(60^(@) + 39.2^(@))/(2))/(sin 30^(@)) = (sin 49.6^(@))/(1//2) = 1.523`
`omega = (mu_(v) - mu_( r))/(mu_(y) - 1) = (1.523 - 1.514)/(1.5184 - 1) = (0.009)/(0.5184) = 0.018`