Question

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

• A. behaves as concave lens if $|f_{convex}|>|f_{concave}|$
• B. behaves as concave lens if $|f_{convex}| < |f_{concave}|$
• C. behaves as convex lens if $|f_{convex}|>|f_{concave}|$
• D. Focal length of the lens system will change if the positions of two lenses are interchanged

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For thin lenses in contact, the equivalent power is the sum of individual powers: $P_{eq} = P_1 + P_2 \implies \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$. 
Step 2: Detailed Explanation: 
Let $f_1 = f_{convex} = +f_1$ and $f_2 = f_{concave} = -f_2$. 
\[ \frac{1}{F} = \frac{1}{f_1} - \frac{1}{f_2} = \frac{f_2 - f_1}{f_1 f_2} \] 
The combination behaves as a concave lens if $F$ is negative ($P_{eq} < 0$). 
$F < 0 \implies \frac{1}{f_1} - \frac{1}{f_2} < 0 \implies \frac{1}{f_1} < \frac{1}{f_2} \implies f_1>f_2$. 
This means $|f_{convex}|>|f_{concave}|$. 
Similarly, it behaves as a convex lens if $|f_{convex}| < |f_{concave}|$. 
Step 3: Final Answer: 
Statement (A) is correct.