Question

A deviation of $2^{\circ }$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as $0.02$ and $0.03$ respectively and refractive index for yellow light for these glasses are $1.5$ and $1.6$ respectively. The refracting angles for crown glass prism will be ${}^{\circ }$(in degree).
(Round off to the Nearest Integer)

Answer 1

In achromatic combination, dispersion is zero but deviation is non-zero.
Net deviation is given as: $${\delta }_{net}=({\mu }_1-1)A_1-({\mu }_2-1)A_2$$$\Rightarrow 2^{\circ }=0.5A_1-0.6A_2$ ...(1)

Condition for dispersion to be zero is given as: $${\omega }_1({\mu }_1-1)A_1={\omega }_2({\mu }_2-1)A_2$$$\Rightarrow 0.02\left(0.5\right)A_1=0.03\left(0.6\right)A_2$
$\Rightarrow 10A_1=18A_2$ ...(2)

From equation (1) and (2):
$2^{\circ }=\frac{A_1}{2}-\frac{A_1}{3}$
$\therefore A_1={12}^{\circ }$