Chromatic aberration is absent if two thin le | vedclass

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(A) For two thin lenses in contact,the equivalent focal length $F$ is given by $\frac{1}{F} = \frac{1}{F_1} + \frac{1}{F_2}$.Chromatic aberration is a

Vedclass · Accepted Answer

$(\omega_1 / F_1) + (\omega_2 / F_2) = 0$

Vedclass · Answer

(A) For two thin lenses in contact,the equivalent focal length $F$ is given by $\frac{1}{F} = \frac{1}{F_1} + \frac{1}{F_2}$.Chromatic aberration is absent (achromatic doublet) when the change in equivalent power with respect to wavelength is zero,i.e.,$\frac{d}{d\lambda} (\frac{1}{F}) = 0$.Since $\frac{1}{F} = \frac{1}{F_1} + \frac{1}{F_2}$,we have $\frac{d}{d\lambda} (\frac{1}{F_1}) + \frac{d}{d\lambda} (\frac{1}{F_2}) = 0$.We know that $\omega = \frac{d(1/F)}{d(1/F_{avg})} = \frac{1/F_v - 1/F_r}{1/F_y}$,which implies $\frac{d(1/F)}{d\lambda} = -\frac{\omega}{F}$.Substituting this,we get $-\frac{\omega_1}{F_1} - \frac{\omega_2}{F_2} = 0$,which simplifies to $\frac{\omega_1}{F_1} + \frac{\omega_2}{F_2} = 0$.

Chromatic aberration is absent if two thin lenses in contact satisfy the condition:

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