MHT CET · Physics · Ray Optics

A convex lens of focal length ‘f’ is placed in contact with a concave lens of the same focal length. The equivalent focal length of the combination is

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

Verified Solution

Answer & Solution

Correct Answer

(B) Infinity

Step-by-step Solution

Detailed explanation

Given, focal length of convex lens,

f_{1} = f

and focal length of concave lens,

f_{2} = - f

.
The focal length of combination, when two lenses are in contact is given by

\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}

Substituting given value in Eq. (i). We get

\Rightarrow \frac{1}{f} = \frac{1}{f} - \frac{1}{f} = 0 \Rightarrow f = \infty

Hence, the equivalent focal length of the combination is infinity.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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