# A deviation

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 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 (in degree) (Round off to the Nearest Integer)

Solution:

(12)

$\omega_{1}=0.02 ; \mu_{1}=1.5 ; \quad \omega_{2}=0.03 ; \mu_{2}=1.6$

Achromatic combination

$\therefore \theta_{\mathrm{net}}=0$

$\theta_{1}-\theta_{2}=0$

$\theta_{1}=\theta_{2}$

$\omega_{1} \delta_{1}=\omega_{2} \delta_{2}$

$\& \delta_{\text {net }}=\delta_{1}-\delta_{2}=2^{\circ}$

$\delta_{1}-\frac{\omega_{1} \delta_{1}}{\omega_{2}}=2^{\circ}$

$\delta_{1}\left(1-\frac{\omega_{1}}{\omega_{2}}\right)=2^{\circ}$

$\delta_{1}\left(1-\frac{2}{3}\right)=2^{\circ}$

$\delta_{1}=6^{\circ}$

$\delta_{1}=\left(\mu_{1}-1\right) \mathrm{A}_{1}$

$6^{\circ}=(1.5-1) \mathrm{A}_{1}$

$\mathrm{A}_{1}=12^{\circ}$