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 $24 \,cm , 30\, cm$ and $32\, cm$ respectively. The dispersive power of the material of the lens is________.

Answer 1

Considering yellow to be mean colour,
$\omega=\frac{\delta_{v}-\delta_{o}}{\delta_{y}}$

From figure,
$\tan \delta \approx \delta$
$\ldots$..(For small angle)
$\therefore \delta_{v} =\frac{x}{v_{v}}, \delta_{0}=\frac{x}{v_{0}}, \delta_{y}=\frac{x}{v_{y}} $
$\therefore \omega =\frac{\frac{x}{v_{v}}-\frac{x}{v_{0}}}{\frac{x}{v_{y}}}=\frac{x \frac{v_{0}-v_{v}}{v_{0} v_{v}}}{\frac{x}{v_{y}}}$
$=\frac{32-24}{32 \times 24} \times 30$
$=\frac{5}{16}=0.3125 \approx 0.31$
$\ldots$ (Rounding off to $2$ decimal places)