2023 Ray Optics and Optical InstrumentsCombination of Thin Lenses in Contact Easy Question 2 of 2 in Combination of Thin Lenses in Contact

Two thin lenses are of same focal lengths ($f$), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:

A Infinite
B Zero
C $\frac{f}{4}$
D $\frac{f}{2}$

The answer is A.

Solution

$\frac{1}{f_{comb}}=\frac{1}{f}-\frac{1}{f}=0$, so $f_{comb}=\infty$.

$F_{convex}=f$, $F_{concave}=-f$ $\frac{1}{f_{comb}}=\frac{1}{F_{convex}}+\frac{1}{F_{concave}}=\frac{1}{f}-\frac{1}{f}$ $\Rightarrow f_{comb}=\infty$

Concept convex plus concave of equal f

Combination of Thin Lenses in Contact in past papers

2 questions from this chapter have appeared across 2 exam years.