A glass prism deviates the red and violet ray | vedclass

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Question

(A) The dispersive power $\omega$ of a prism is given by the formula $\omega = \frac{\delta_v - \delta_r}{\delta_y}$,where $\delta_v$ is the deviation

Vedclass · Accepted Answer

$5: 6$

Vedclass · Answer

(A) The dispersive power $\omega$ of a prism is given by the formula $\omega = \frac{\delta_v - \delta_r}{\delta_y}$,where $\delta_v$ is the deviation for violet light,$\delta_r$ is the deviation for red light,and $\delta_y$ is the mean deviation,calculated as $\delta_y = \frac{\delta_v + \delta_r}{2}$.For the first prism:$\delta_v = 11^{\circ}$,$\delta_r = 9^{\circ}$.$\delta_{y1} = \frac{11 + 9}{2} = 10^{\circ}$.$\omega_1 = \frac{11 - 9}{10} = \frac{2}{10} = \frac{1}{5}$.For the second prism:$\delta_v = 13^{\circ}$,$\delta_r = 11^{\circ}$.$\delta_{y2} = \frac{13 + 11}{2} = 12^{\circ}$.$\omega_2 = \frac{13 - 11}{12} = \frac{2}{12} = \frac{1}{6}$.The ratio of the dispersive power of the second prism to the first prism is $\frac{\omega_2}{\omega_1} = \frac{1/6}{1/5} = \frac{5}{6}$.Thus,the ratio is $5: 6$.

$A$ glass prism deviates the red and violet rays through $9^{\circ}$ and $11^{\circ}$ respectively. $A$ second prism of equal angle deviates them through $11^{\circ}$ and $13^{\circ}$ respectively. The ratio of dispersive power of the second prism to the first prism is

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