Question

A person cannot see objects clearly beyond 40 cm. The power of the lens to correct vision is

• A. + 2.5 D
• B. - 2.5 D
• C. +4 D
• D. -4 D

Answer 1

The Correct Option is B

The person cannot see objects clearly beyond 40 cm, which indicates that they are suffering from myopia (nearsightedness). In myopia, the far point of the eye is closer than infinity, and the corrective lens required is a concave lens (negative power) to diverge the incoming light so that it appears to come from the person's far point.

Step 1: Use the lens formula to find the focal length of the corrective lens.

The lens formula is:

\[ P = \frac{1}{f}, \]

where \( P \) is the power of the lens in diopters (D), and \( f \) is the focal length in meters. For a concave lens used to correct myopia, the focal length is negative.

The far point of the person is 40 cm (0.4 m), which means the image formed by the lens must be at the far point when the object is at infinity. Thus:

\[ f = -0.4 \, \text{m}. \]

Step 2: Calculate the power of the lens.

Substitute \( f = -0.4 \, \text{m} \) into the formula for power:

\[ P = \frac{1}{f} = \frac{1}{-0.4} = -2.5 \, \text{D}. \]

Final Answer: The power of the lens required to correct the vision is \( \mathbf{-2.5 \, \text{D}} \), which corresponds to option \( \mathbf{(2)} \).