Assertion: Two convex lenses joined together | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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)

Vedclass · Accepted Answer

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

Vedclass · Answer

(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.

Similar Questions

Two thin lenses whose powers are $+2 \ D$ and $-4 \ D$ respectively are combined. The power of the combination is:

In the given optical instrument,how can a third lens of the same focal length be inserted to increase the light-collecting efficiency without changing the positions of the object and the image? Calculate the position of that lens.

An achromatic combination of lenses produces

Two thin lenses of focal lengths $20 \ cm$ and $25 \ cm$ are placed in contact. The effective power of the combination is (in $D$)

It is desired to make an achromatic combination of two lenses ($L_1$ and $L_2$) made of materials having dispersive powers $\omega_1$ and $\omega_2$ $(< \omega_1)$. If the combination of lenses is converging,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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.