Question

A person can see clearly objects only when they lie between $50\,cm$ and $400\,cm$ from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be

• A. convex, + 2.25 diopter
• B. concave, - 0.25 diopter
• C. concave, - 0.2 diopter
• D. convex, + 0.15 diopter

Answer 1

The Correct Option is B

Lens Power Calculation 

The lens formula is given by:

\(\frac{1}{v} - \frac{1}{u} = P\)

Where: - \( v \) is the image distance, - \( u \) is the object distance, - \( P \) is the power of the lens.

Step-by-Step Calculation:

We are given the following values: - The object distance \( u = -4 \, \text{m} \) (negative for a real object), - The image distance \( v = \infty \) (infinity for an image formed at infinity).

Substitute these values into the lens formula:

\(\frac{1}{-4} - \frac{1}{\infty} = P\)

Simplifying:

\(P = - 0.25 \, \text{D}\)

Since the power is negative, the lens is a concave lens.

Conclusion:

The correct answer is (B): Concave, -0.25 diopter.