Question

A convex and a concave lens are placed in contact. The focal lengths \( (F) \) of both are the same. The combination will behave:

• A. as a concave lens.
• B. as a convex lens.
• C. as a planoconvex lens.
• D. as a plane plate.

Hint:

Powers add for lenses in contact; equal-magnitude convex \((+1/F)\) and concave \((-1/F)\) give zero net power, i.e. infinite focal length.

Answer 1

The Correct Option is D

Step 1: Power of lenses in contact.
When two thin lenses are placed in contact, their powers add:
\[ P = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2}. \]
Step 2: Assign signs.
For a convex lens the focal length is positive: \( f_1 = +F \). For a concave lens it is negative: \( f_2 = -F \).

Step 3: Add the powers.
\[ P = \frac{1}{+F} + \frac{1}{-F} = \frac{1}{F} - \frac{1}{F} = 0. \]
Step 4: Interpret the result.
Zero net power means the combined focal length is infinite:
\[ \frac{1}{F_{comb}} = 0 \Rightarrow F_{comb} = \infty. \]
A system of infinite focal length neither converges nor diverges light; it just transmits rays straight, exactly like a plane glass plate. So option (iv) is correct, and (i), (ii), (iii) are wrong because they all imply a finite non-zero power.

\[\boxed{P = 0 \Rightarrow \text{plane plate}}\]