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  4. A prism of a certain angle deviates the red and blue rays by 8° and 12° respectively. Another prism of the same angle deviates the red and blue rays by 10° and 14° respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

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Q. A prism of a certain angle deviates the red and blue rays by $8^\circ$ and $12^\circ$ respectively. Another prism of the same angle deviates the red and blue rays by $10^\circ$ and $14^\circ$ respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

KCETKCET 2007Ray Optics and Optical Instruments

Solution:

Dispersive power, $\omega=\frac{\delta_{B}-\delta_{R}}{\delta}$
For 1st prism,
$\omega_{1} =\frac{\delta_{B}-\delta_{R}}{\delta} $
$=\frac{12^{\circ}-8^{\circ}}{10^{\circ}}=\frac{2}{5} $
where $ \delta =\frac{\delta_{B}+\delta_{R}}{2}$
Similarly, for 2 nd prism,
$\omega_{2}=\frac{14^{\circ}-10^{\circ}}{12}=\frac{1}{3}$
$\frac{\omega_{1}}{\omega_{2}}=\frac{2}{5} \times \frac{3}{1}=\frac{6}{5}$