Assertion: Two convex lenses joined together | vedclass

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(A) The condition for an achromatic doublet is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$. Since $\omega_1$ and $\omega_2$ (dispersive powers)

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If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

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(A) The condition for an achromatic doublet is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$. Since $\omega_1$ and $\omega_2$ (dispersive powers) are always positive for any material,for the sum to be zero,one of the focal lengths ($f_1$ or $f_2$) must be negative. $A$ negative focal length corresponds to a concave lens. Therefore,to form an achromatic combination,one lens must be convex and the other must be concave. Two convex lenses cannot satisfy this condition because both $f_1$ and $f_2$ would be positive,making the sum $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2}$ always positive (greater than zero). Thus,the Assertion is correct and the Reason is also correct,providing the correct explanation.

Assertion: Two convex lenses joined together cannot produce an achromatic combination.
Reason: The condition for achromatism is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where symbols have their usual meaning.

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Assertion: Two convex lenses joined together cannot produce an achromatic combination.Reason: The condition for achromatism is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where symbols have their usual meaning.