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

Concept:
Lens maker formula for a thin lens is: \[ P=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \] So power is proportional to a combination of reciprocals of radii. ip

Step 1: Express power in reciprocal form.
Ignoring constant factor \((\mu-1)\), power is proportional to: \[ \frac{1}{R_1}\pm \frac{1}{R_2} \] ip

Step 2: Combine the terms.
\[ \frac{1}{R_1}+\frac{1}{R_2} = \frac{R_1+R_2}{R_1R_2} \] So the proportionality form among the given options is: \[ \frac{R_1+R_2}{R_1R_2} \] ip Hence, the correct answer is:
\[ \boxed{(D)\ \frac{R_1+R_2}{R_1R_2}} \]