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

To solve this problem, we need to analyze the given specifications and determine the lens required to correct this person's vision to achieve clear vision up to infinity.

1. **Understanding the given condition:** The person can see clearly between $50\,\text{cm}$ (near point) and $400\,\text{cm}$ (far point). In order to correct his far point to infinity, a lens is needed.

2. **Type of lens required:** Since the farthest point for clear vision is finite and needs to be adjusted to infinity, a concave lens is needed. Concave lenses help people with myopia (nearsightedness) see distant objects clearly.

3. **Formula for calculating lens power:**

To find the necessary lens power:

v = \text{Infinity (∞)} \ \ \text{and} \ \ u = -400\,\text{cm}

Using the lens formula:

\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}

Substituting the values:

\dfrac{1}{f} = \dfrac{1}{\infty} - \dfrac{1}{-400} = 0 + \dfrac{1}{400} = \dfrac{1}{400}

Thus, the focal length f is 400\,\text{cm} or 4\,m.

4. **Calculating power of the lens:** Power P is given by:

P = \dfrac{1}{f \ (\text{in meters})}

Substituting the value of f:

P = \dfrac{1}{4} = -0.25\,\text{diopters}

Note the negative sign indicates that the lens is concave.

5. **Conclusion:** The correct answer is "concave, -0.25 diopter". The concave lens helps extend the person's far point to infinity, allowing them to see distant objects clearly.