Question

If focal length of a concave lens is 50 cm, then the power of the lens would be

• A. +5 D
• B. -5 D
• C. +2 D
• D. -2 D

Hint:

Remember the sign conventions for lenses: - Concave (diverging) lens: Focal length is negative, Power is negative. - Convex (converging) lens: Focal length is positive, Power is positive. And always convert the focal length to meters before calculating power in dioptres.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The power of a lens is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of the focal length of the lens. The sign convention for focal length is crucial.

Step 2: Key Formula or Approach:
The power \(P\) of a lens is given by: \[ P = \frac{1}{f} \] where the focal length \(f\) must be expressed in meters for the power \(P\) to be in dioptres (D). By sign convention, a concave lens (diverging lens) has a negative focal length.

Step 3: Detailed Explanation:
Given data:
Lens type: Concave lens. Focal length magnitude = 50 cm.

Step 1: Apply sign convention.
For a concave lens, the focal length is negative. So, \(f = -50 \, \text{cm}\).

Step 2: Convert focal length to meters.
\[ f = -50 \, \text{cm} = -0.5 \, \text{m} \]

Step 3: Calculate the power.
\[ P = \frac{1}{f} = \frac{1}{-0.5 \, \text{m}} = -2 \, \text{D} \]

Step 4: Final Answer:
The power of the concave lens is -2 D.