Question

The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens.

Answer 1

The focal length of lens is given by,

$\frac{1}{f}=(\mu -1).\frac{1}{R_1}-\frac{1}{R_2}$

$\Rightarrow (\mu -1)=\frac{1}{f}\times \frac{1}{\frac{1}{R_1}-\frac{1}{R_2}}$

$=\frac{k}{f}$ . . . . (i)

So, ${\mu }_r-1=\frac{k}{100}$ . . . . (ii)

${\mu }_y-1=\frac{k}{98}$ . . . . (ii)

and ${\mu }_v-1=\frac{k}{96}$ . . . .(ii)

So, Dispersive power $=\omega$

$=\frac{{\mu }_v-{\mu }_r}{{\mu }_y-1}$

$=\frac{({\mu }_v-1)-({\mu }_r-1)}{({\mu }_y-1)}$

$=\frac{\frac{k}{96}-\frac{k}{100}}{\frac{k}{98}}=\frac{98\times 4}{9600}$

= 0.0408