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

Concept Understanding: Lens power quantifies its light convergence/divergence capability, defined as the reciprocal of its focal length. Focal length sign convention is critical.

Formula/Approach: Lens power \(P\) is calculated as \( P = \frac{1}{f} \). For power \(P\) in dioptres (D), focal length \(f\) must be in meters. A concave lens (diverging) has a negative focal length.

Detailed Explanation: Data: Type: Concave lens. Focal length magnitude: 50 cm.

Sign Convention Application: Concave lenses have negative focal lengths. Thus, \(f = -50 \, \text{cm}\).

Focal Length Conversion: \( f = -50 \, \text{cm} = -0.5 \, \text{m} \)

Power Calculation: \( P = \frac{1}{f} = \frac{1}{-0.5 \, \text{m}} = -2 \, \text{D} \)

Result: The concave lens power is -2 D.