Question

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is:

• A. (+5D)
• B. (+20D)
• C. (+2D)
• D. infinity

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The focal length of a lens depends on the refractive index of its material and the radii of curvature of its two surfaces.
Once the focal length (\(f\)) is determined, the power (\(P\)) of the lens is calculated as the reciprocal of the focal length in meters.
Key Formula or Approach:
1. Lens Maker's Formula:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
2. Power Formula:
\[ P = \frac{1}{f(\text{m})} = \frac{100}{f(\text{cm})} \]
Step 2: Detailed Explanation:
1. Define parameters with sign convention:
For a biconvex lens:
First surface is convex \(\implies R_1 = +20 \text{ cm}\).
Second surface is concave from the inside \(\implies R_2 = -20 \text{ cm}\).
Refractive index \(\mu = 1.5\).
2. Calculate focal length:
\[ \frac{1}{f} = (1.5 - 1) \left( \frac{1}{20} - \frac{1}{-20} \right) \]
\[ \frac{1}{f} = (0.5) \left( \frac{1}{20} + \frac{1}{20} \right) \]
\[ \frac{1}{f} = 0.5 \times \frac{2}{20} = 0.5 \times \frac{1}{10} = \frac{1}{20} \text{ cm}^{-1} \]
So, \(f = 20 \text{ cm}\).
3. Calculate Power:
\[ P = \frac{100}{f(\text{cm})} = \frac{100}{20} = +5 \text{ Dioptre (D)} \]
Step 3: Final Answer:
The power of the lens is \(+5\) D.