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

An object $AB$ is placed $15 \text{ cm}$ on the left of a convex lens $P$ of focal length $10 \text{ cm}$. Another convex lens $Q$ is now placed $15 \text{ cm}$ to the right of lens $P$. If the focal length of lens $Q$ is $15 \text{ cm}$, the final image is . . . . . . .

Two lenses of power $+10D$ and $-5D$ are placed in contact. At what distance (in $cm$) should an object be held from the lens combination to obtain a virtual image of magnification $2$?

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.

Two thin convex lenses of focal lengths $20 \; cm$ and $25 \; cm$ are placed in contact. The effective power of the combination is:

The focal length of a combination of lenses formed with lenses having powers of $+2.50 \ D$ and $-3.75 \ D$ will be .... $cm$.

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.