Question

A parallel beam of white light falls on a convex lens. Images of violet, yellow and orange light are formed on the other side of the lens at distances $24cm,30cm$ and $32cm$ respectively. The dispersive power of the material of the lens is________.

Answer 1

Answer: 0.31

Considering yellow to be mean colour,
$\omega =\frac{{\delta }_v-{\delta }_o}{{\delta }_y}$

From figure,
$\tan \delta \approx \delta$
$\dots$..(For small angle)
$\therefore {\delta }_v=\frac{x}{v_v},{\delta }_0=\frac{x}{v_0},{\delta }_y=\frac{x}{v_y}$
$\therefore \omega =\frac{\frac{x}{v_v}-\frac{x}{v_0}}{\frac{x}{v_y}}=\frac{x\frac{v_0-v_v}{v_0{v}_v}}{\frac{x}{v_y}}$
$=\frac{32-24}{32\times 24}\times 30$
$=\frac{5}{16}=0.3125\approx 0.31$
$\dots$ (Rounding off to $2$ decimal places)