Question

Two thin lenses having $\text{R}_1, \text{R}_2$ as the radii of curved surfaces are kept coaxially together. Their power is proportional to}

• A. $\text{R}_1 + \text{R}_2$
• B. $\text{R}_1 - \text{R}_2$
• C. $\frac{\text{R}_1\text{R}_2}{\text{R}_1+\text{R}_2}$
• D. $\frac{R_1+R_2}{R_1R_2}$

Hint:

If a formula has reciprocal radii, combine them into a single fraction before matching the option.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The power of a lens is the reciprocal of its focal length, determined by the Lens Maker's Formula.
Step 2: Key Formula or Approach:
$P = \frac{1}{f} = (\mu - 1) \left[ \frac{1}{R_1} - \frac{1}{R_2} \right]$.
Step 3: Detailed Explanation:
The term in brackets can be simplified as $\frac{R_2 - R_1}{R_1 R_2}$. Taking magnitude or for standard biconvex lens signs ($R_2$ is negative), the expression becomes proportional to $\frac{R_1 + R_2}{R_1 R_2}$.
Step 4: Final Answer:
Power is proportional to $\frac{R_1+R_2}{R_1R_2}$.