Question

The power of a corrective lens is -4.0 D . The lens is

• A. convex lens of focal length + 25 cm
• B. concave lens of focal length -25 cm
• C. convex lens of focal length +4 cm
• D. concave lens of focal length -4 cm
• E. convex lens of focal length +20 cm

Answer 1

The Correct Option is B

The power \( P \) of a lens is related to its focal length \( f \) by the formula: \[ P = \frac{1}{f} \] where \( P \) is the power in diopters (D) and \( f \) is the focal length in meters. Given that the power of the corrective lens is \( P = -4.0 \, \text{D} \), we can find the focal length using the formula: \[ f = \frac{1}{P} \] Substituting \( P = -4.0 \, \text{D} \): \[ f = \frac{1}{-4.0} = -0.25 \, \text{m} = -25 \, \text{cm} \]

The correct option is (B) : concave lens of focal length -25 cm

Answer 2

The power of a lens (P) is related to its focal length (f) in meters by the formula:
 
\( P = \frac{100}{f(\text{in cm})} \Rightarrow f = \frac{100}{P} \)

Given: P = -4.0 D
\( f = \frac{100}{-4} = -25 \, \text{cm} \)

➤ A negative power indicates a concave lens.

✅ Correct answer: concave lens of focal length -25 cm

❌ Other options are incorrect because:
– Convex lenses have positive power.
– Focal length must match the power correctly.