Question

For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm. The refractive index of the material is :

• A. 1.2
• B. 1.4
• C. 1.5
• D. 1.8

Answer 1

The Correct Option is C

Using the lens maker’s formula:
\[\frac{1}{f} = \left( \frac{\mu_{\text{lens}}}{\mu_{\text{air}}} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]
Given:
\[f = 20 \, \text{cm}, \quad R_1 = 15 \, \text{cm}, \quad R_2 = -30 \, \text{cm}\]
Substitute into the formula:
\[\frac{1}{20} = (\mu - 1) \left( \frac{1}{15} - \frac{1}{-30} \right)\]
Simplify the expression:
\[\frac{1}{20} = (\mu - 1) \left( \frac{3}{30} \right)\]
\[\Rightarrow \mu - 1 = \frac{1}{2}\]
\[\Rightarrow \mu = 1 + \frac{1}{2} = \frac{3}{2} = 1.5\]