Question

The minimum deviations suffered by red, yellow and violet beams passing passing through an equilateral transparent prism are `38.4^@, 38.76@ and 39.2^@` respectively. Calculate the dispersive power of the medium.

Answer 1

Correct Answer - `0.018`
As the prism is equilaterial, `:. A = (180)/(3) = 60^@`
`(delta_m)_r = 38.4^@, (delta_m)_y = 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`.