Question

A convex lens has radius of curvature \( R = 40 \, \text{cm} \) for both surfaces and refractive index \( \mu = 1.5 \). Find the focal length.

• A. \( 40 \, \text{cm} \)
• B. \( 20 \, \text{cm} \)
• C. \( 80 \, \text{cm} \)
• D. \( 30 \, \text{cm} \)

Hint:

Apply lens maker’s formula: both radii are equal and opposite for a symmetrical convex lens.

Answer 1

The Correct Option is A

Lens Maker’s Formula: \[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = (1.5 - 1) \left( \frac{1}{40} - \frac{-1}{40} \right) = 0.5 \cdot \frac{2}{40} = \frac{1}{40} \Rightarrow f = 40 \, \text{cm} \]