Question

A plano-convex lens is made of refractive index of 1.6. The radius of curvature of the curved surface is $60~\mathrm{cm}$. The focal length of the lens is

• A. $400\mathrm{cm}$
• B. $200\mathrm{cm}$
• C. $100\mathrm{cm}$
• D. $50\mathrm{cm}$

Hint:

For plano-convex lens, $\frac{1}{f} = \frac{\mu - 1}{R_1}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For plano-convex lens, $R_2 = \infty$. Lens maker's formula: $\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$.
Step 2: Detailed Explanation:
$R_1 = 60$ cm, $R_2 = \infty$. $\frac{1}{f} = (1.6 - 1)\left(\frac{1}{60} - 0\right) = 0.6 \times \frac{1}{60} = \frac{1}{100}$. So $f = 100$ cm.
Step 3: Final Answer:
The focal length is $100$ cm.