A person can see objects clearly only when they lie between `50cm` 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

Options

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

Answer

To solve the problem, we need to determine the type and power of the correcting lens required for a person who can only see objects clearly between 50 cm and 400 cm from their eyes. The goal is to increase the maximum distance of distinct vision to infinity.

### Step-by-Step Solution:

1. **Identify the given data:**
- The near point (closest distance of distinct vision) is \( u = -50 \) cm (negative because it is on the same side as the object).
- The far point (farthest distance of distinct vision) is \( v = -400 \) cm (also negative for the same reason).

2. **Understand the requirement:**
- We want to correct the vision such that the maximum distance of distinct vision becomes infinity (\( v = -\infty \)).

3. **Use the lens formula:**
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Here, we will substitute \( v = -\infty \) and \( u = -400 \) cm.

4. **Substituting the values:**
\[ \frac{1}{f} = \frac{1}{-\infty} - \frac{1}{-400} \]
Since \( \frac{1}{-\infty} = 0 \), we have:
\[ \frac{1}{f} = 0 + \frac{1}{400} \]
Thus,
\[ \frac{1}{f} = \frac{1}{400} \]

5. **Calculate the focal length \( f \):**
\[ f = 400 \text{ cm} \]
Since we are correcting for a person who can only see up to 400 cm, we need a lens that brings this distance to infinity. Therefore, the focal length will be negative:
\[ f = -400 \text{ cm} \]

6. **Calculate the power of the lens:**
The power \( P \) of the lens is given by:
\[ P = \frac{1}{f} \text{ (in meters)} \]
First, convert \( f \) into meters:
\[ f = -400 \text{ cm} = -4 \text{ m} \]
Now, calculate the power:
\[ P = \frac{1}{-4} = -0.25 \text{ diopters} \]

7. **Determine the type of lens:**
Since the power is negative, the lens required is a **concave lens**.

### Final Answer:
The person needs a **concave lens** with a power of **-0.25 diopters**.

---