For a person near point of vision is 100cm. Then the power of lens he must wear so as to have normal vision, should be

Options

A. `+1 D`
B. `-1 D`
C. `+3 D`
D. `-3D `

Explanation

To solve the problem of determining the power of the lens a person must wear to achieve normal vision, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Values**:
- The near point of vision (the closest distance at which the eye can see clearly) is given as \( D = 100 \, \text{cm} \).
- The minimum distance of distinct vision (the standard near point for normal vision) is \( d = 25 \, \text{cm} \).

2. **Convert Distances to Appropriate Signs**:
- For lens formula calculations, we use the sign convention:
- Object distance \( u = -d = -25 \, \text{cm} \) (since the object is on the same side as the incoming light).
- Image distance \( v = -D = -100 \, \text{cm} \) (since the image is formed on the same side as the object).

3. **Apply the Lens Formula**:
- The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
- Substituting the values:
\[ \frac{1}{f} = \frac{1}{-100} + \frac{1}{-25} \]

4. **Calculate the Right-Hand Side**:
- Calculate \( \frac{1}{-100} + \frac{1}{-25} \):
\[ \frac{1}{-100} + \frac{1}{-25} = -\frac{1}{100} - \frac{4}{100} = -\frac{5}{100} = -\frac{1}{20} \]

5. **Find the Focal Length**:
- From the lens formula:
\[ \frac{1}{f} = -\frac{1}{20} \implies f = -20 \, \text{cm} \]

6. **Convert Focal Length to Meters**:
- Convert \( f \) to meters:
\[ f = -20 \, \text{cm} = -0.2 \, \text{m} \]

7. **Calculate 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:
\[ P = \frac{1}{-0.2} = -5 \, \text{D} \]

8. **Interpret the Result**:
- Since the power is negative, this indicates that the lens required is a concave lens, which is used for correcting myopia (nearsightedness).

### Final Answer
The power of the lens the person must wear to achieve normal vision is \( -5 \, \text{D} \).