The focal lengths of a thin lens for red and violet light are 90.0 cm and 86.4cm respectively. Find the dispersive power of the material of the lens. Make appropriate assumptions.

Explanation

We have
`(1)/(f) = (mu-1) ((1)/(R_1) - (1)/(R_2))`
`or `mu - 1 = (1)/(f). (1)/((1)/(R_1) - (1)/(R_2)) = (K)/(f).`
Thus, `mu_(upsilon) -1 = (K)/(f_(upsilon))`
and `mu_r - 1=(K)/(f_r)`
so that `mu_(upsilon) - mu_r = K((1)/(f_(upsilon)) - (1)/(f_r))`
`=K[(1)/(85.4 cm) - (1)/(90cm)] =Kxx4.6 xx 10^(-4) cm^(-1)`
Also, we can assume that
`mu_y -1 = (mu_(upsilon) + mu_r)/(2) -1 = (mu_(upsilon) - 1)/(2) + (mu_(upsilon)-1)/(2)`
`(K)/(2) ((1)/(f_(upsilon) + (1)/(f_r))`
`=(K)/(2) [(1)/(86.4 cm) + (1)/(90cm)] = Kxx1.1xx10^(-2)cm^O(-1)`
Thus, the dispervise power of the meterial of the lens
`omega= (mu_(upsilon) - mu_r)/(mu_y - 1) = (4.6xx 10^(-4))/(1.1xx10^(-2)) = 0.042.`