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

Applying the lens maker’s formula:
\[\frac{1}{f} = \left( \frac{\mu_{\text{lens}}}{\mu_{\text{air}}} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\]
With the given values:
\[f = 20 \, \text{cm}, \quad R_1 = 15 \, \text{cm}, \quad R_2 = -30 \, \text{cm}\]
Substitution into the formula yields:
\[\frac{1}{20} = (\mu - 1) \left( \frac{1}{15} - \frac{1}{-30} \right)\]
Simplification of the expression proceeds as follows:
\[\frac{1}{20} = (\mu - 1) \left( \frac{3}{30} \right)\]
\[\Rightarrow \mu - 1 = \frac{1}{2}\]
\[\Rightarrow \mu = 1 + \frac{1}{2} = \frac{3}{2} = 1.5\]