Two lenses having focal lengths in the ratio | vedclass

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Question

(A) For a combination of two thin lenses to produce no net dispersion (achromatic doublet),the condition is given by $\frac{\omega_1}{f_1} + \frac{\om

Vedclass · Accepted Answer

$2:3$

Vedclass · Answer

(A) For a combination of two thin lenses to produce no net dispersion (achromatic doublet),the condition is given by $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$.This implies $\frac{\omega_1}{\omega_2} = -\frac{f_1}{f_2}$.Given the ratio of focal lengths is $\frac{f_1}{f_2} = \frac{2}{3}$.Substituting this value,we get $\frac{\omega_1}{\omega_2} = -\frac{2}{3}$.Since dispersive power is a positive quantity,we consider the magnitude of the ratio,which is $2:3$.

Two lenses having focal lengths in the ratio $f_1:f_2 = 2:3$ are combined to produce no net dispersion. Find the ratio of the dispersive powers of the glasses used.

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