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

Options

A. convex,+2.25D
B. convex,+0.25D
C. convex,+0.2D
D. convex,+0.15D

Explanation

To solve the problem, we need to determine the type of lens that a person should use to increase their maximum distance of distinct vision from 400 cm to infinity. Here’s the step-by-step solution:

### Step 1: Understanding the Problem
The person can see clearly objects only between 50 cm (0.5 m) and 400 cm (4 m). To see objects at a distance of infinity, we need to adjust the vision using a lens.

### Step 2: Lens Formula
We will use the lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( f \) is the focal length of the lens,
- \( v \) is the image distance,
- \( u \) is the object distance.

### Step 3: Setting Up the Distances
We want the image to form at the maximum distance of distinct vision, which is 400 cm (or 4 m). When the object is at infinity, we can set:
- \( v = -4 \, \text{m} \) (the negative sign indicates that the image is virtual and on the same side as the object),
- \( u = -\infty \) (since the object is at infinity).

### Step 4: Applying the Lens Formula
Substituting the values into the lens formula:
\[ \frac{1}{f} = \frac{1}{-4} - \frac{1}{-\infty} \]
Since \( \frac{1}{-\infty} = 0 \), the equation simplifies to:
\[ \frac{1}{f} = -\frac{1}{4} \]

### Step 5: Finding the Focal Length
From the equation, we can find the focal length:
\[ f = -4 \, \text{m} \]

### Step 6: Calculating the Power of the Lens
The power \( P \) of a lens is given by:
\[ P = \frac{1}{f} \, (\text{in meters}) \]
Substituting the focal length:
\[ P = \frac{1}{-4} = -0.25 \, \text{diopters} \]

### Step 7: Identifying the Type of Lens
The negative power indicates that the lens is a concave lens.

### Conclusion
To increase the maximum distance of distinct vision to infinity, the person needs to use a **concave lens** with a power of **-0.25 diopters**.

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