A glass prism A deviates the red and blue ray | vedclass

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Question

(C) The dispersive power $\omega$ is given by the formula $\omega = \frac{\delta_v - \delta_R}{\delta_y}$,where $\delta_y = \frac{\delta_v + \delta_R}

Vedclass · Accepted Answer

$9:11$

Vedclass · Answer

(C) The dispersive power $\omega$ is given by the formula $\omega = \frac{\delta_v - \delta_R}{\delta_y}$,where $\delta_y = \frac{\delta_v + \delta_R}{2}$ is the mean deviation.For prism $A$:$\delta_y = \frac{12^{\circ} + 10^{\circ}}{2} = 11^{\circ}$.$\omega_A = \frac{12^{\circ} - 10^{\circ}}{11^{\circ}} = \frac{2}{11}$.For prism $B$:$\delta_y = \frac{10^{\circ} + 8^{\circ}}{2} = 9^{\circ}$.$\omega_B = \frac{10^{\circ} - 8^{\circ}}{9^{\circ}} = \frac{2}{9}$.The ratio of their dispersive powers is $\frac{\omega_A}{\omega_B} = \frac{2/11}{2/9} = \frac{9}{11}$.

$A$ glass prism $A$ deviates the red and blue rays through $10^{\circ}$ and $12^{\circ}$ respectively. $A$ second prism $B$ deviates them through $8^{\circ}$ and $10^{\circ}$ respectively. The ratio of their dispersive powers is ($A$ to $B$):

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