The radius of curvature of the curved side of a plano-convex lens made of glass, having index of refraction 1.64, is 33 cm. What is the focal length of the lens?
A) 52 cm
B) 21 cm
C) -52 cm
D) -21 cm

Question

Quizplus · Accepted Answer

The focal length $ f $ of a plano-convex lens can be calculated using the lens maker's formula:  $$ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $$  For a plano-convex lens, $ R_2 = \infty $ and $ R_1 = 33 \, \text{cm} $.  Substituting the values:  $$ \frac{1}{f} = (1.64 - 1) \left( \frac{1}{33} - 0 \right) $$  $$ \frac{1}{f} = 0.64 \times \frac{1}{33} $$  $$ f = \frac{33}{0.64} \approx 51.56 \, \text{cm} $$  Thus, the focal length is approximately 52 cm.

The Radius of Curvature of the Curved Side of a Plano-Convex