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  • A deviation of  is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispresive powers of crown and flint glass as 0.02 and 0.03 res

A deviation of 2^{\circ} is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispresive 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 __________(in degree) (rounded off to the nearest integer)
Option: 1 12
Option: 2 13
Option: 3 14
Option: 4 15

Answers (1)

best_answer

Given \omega_{1}=0.02 ; \mu_{1}=1.5 ; \quad \omega_{2}=0.03 ; \mu_{2}=1.6
For Achromatic combination
\\ \theta_{\text {net }}=0 \\ \theta_{1}-\theta_{2}=0 \\ \theta_{1}=\theta_{2} \\ \Rightarrow \omega_{1} \delta_{1}=\omega_{2} \delta_{2} \\ \& \delta_{\text {ret }}=\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} \\ \ \Rightarrow \ \delta_{1}=6^{\circ} \\ \delta_{1}=\left(\mu_{1}-1\right) \mathrm{A}_{1} \\ 6^{\circ}=(1.5-1) \mathrm{A}_{1} \\ \Rightarrow \mathrm{A}_{1}=12^{\circ}

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avinash.dongre

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