A man can see the objects upto a distance of one metre from his eyes. For correcting his eye sight so that he can see an object at infinity, he requires a lens whose power is

Options

A. `+0.5D`
B. `+1.0`
C. `+2.0`
D. `-1.0D`

Explanation

To solve the problem, we need to determine the power of the lens required for a man who can only see objects up to a distance of 1 meter, so that he can see objects at infinity.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The maximum distance at which the man can see clearly (near point) is \( d = 1 \, \text{m} \).
- He wants to see objects at infinity, which means the object distance \( u = -\infty \) (the negative sign indicates that the object is on the same side as the incoming light).

2. **Determine the Image Distance:**
- For the man to see an object at infinity, the image must be formed at his near point, which is \( v = -1 \, \text{m} \) (again, the negative sign indicates that the image is formed on the same side as the object).

3. **Use the Lens Formula:**
- The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
- Substitute the values of \( v \) and \( u \):
\[ \frac{1}{f} = \frac{1}{-1} - \frac{1}{-\infty} \]

4. **Simplify the Equation:**
- Since \( \frac{1}{-\infty} = 0 \), the equation simplifies to:
\[ \frac{1}{f} = -1 - 0 = -1 \]
- Therefore, we find:
\[ f = -1 \, \text{m} \]

5. **Calculate the Power of the Lens:**
- The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{f} \quad \text{(in meters)} \]
- Substitute \( f = -1 \, \text{m} \):
\[ P = \frac{1}{-1} = -1 \, \text{D} \]

6. **Conclusion:**
- The power of the lens required to correct the man's eyesight so that he can see objects at infinity is \( -1 \, \text{D} \).

### Final Answer:
The power of the lens required is \( -1 \, \text{D} \).

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