The power of an achromatic convergent lens co | vedclass

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(B) Given: Total power of the combination $P = P_1 + P_2 = + 2D$.Power of the convex lens $P_1 = + 5D$.Therefore,the power of the concave lens $P_2 =

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$3:5$

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(B) Given: Total power of the combination $P = P_1 + P_2 = + 2D$.Power of the convex lens $P_1 = + 5D$.Therefore,the power of the concave lens $P_2 = P - P_1 = 2D - 5D = - 3D$.For an achromatic combination,the condition is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,which can be written in terms of power as $\omega_1 P_1 + \omega_2 P_2 = 0$.This implies $\frac{\omega_1}{\omega_2} = - \frac{P_2}{P_1}$.Substituting the values: $\frac{\omega_1}{\omega_2} = - \left( \frac{- 3D}{5D} \right) = \frac{3}{5}$.Thus,the ratio of the dispersive power of the convex lens to the concave lens is $3:5$.

The power of an achromatic convergent lens combination consisting of two lenses is $+ 2D$. The power of the convex lens is $+ 5D$. The ratio of the dispersive power of the convex lens to the concave lens will be:

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