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)

Achromatic combination

\(\therefore \theta_{\text {net }}=0\)

\(\theta_{1}-\theta_{2}=0\)

\(\theta_{1}=\theta_{2}\)

\(\omega_{1} \delta_{1}=\omega_{2} \delta_{2}\)

\(\&\, \delta_{\text {net }}=\delta_{1}-\delta_{2}=2^{\circ}\)

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

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

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

\(\delta_{1}=6^{\circ}\)

\(\delta_{1}=\left(\mu_{1}-1\right) A_{1}\)

\(6^{\circ}=(1.5-1) A_{1}\)

\(A_{1}=12^{\circ}\)