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 are $0.02$ 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)
Ans. (12)
$\omega_{1}=0.02 ; \mu_{1}=1.5 ; \omega_{2}=0.03 ; \mu_{2}=1.6$
Achromatic combination
$\therefore \theta_{\text {net }}=0$
$\theta_{1}-\theta_{2}=0$
$\theta_{1}=\theta_{2}$
$\omega_{1} \delta_{1}=\omega_{2} \delta_{2}$
$\& \delta_{\mathrm{net}}=\delta_{1}-\delta_{2}=2^{\circ}$
$\delta_{1}-\frac{\omega_{1} \delta_{1}}{\omega_{2}}=2^{\circ}$
$\delta_{1}\left(1-\frac{\omega_{1}}{\omega_{2}}\right)=2^{\circ}$
$\delta_{1}\left(1-\frac{2}{3}\right)=2^{\circ}$
$\delta_{1}=6^{\circ}$
$\delta_{1}=\left(\mu_{1}-1\right) \mathrm{A}_{1}$
$6^{\circ}=(1.5-1) \mathrm{A}_{1}$
$\mathrm{~A}_{1}=12^{\circ}$