The eye of a man cannot see the object closer than 0.5 m. What power of corrective lens he should use? (The nearest distance of distinct vision is 25 cm)

Options

A. 0.5 D
B. 1 D
C. 2 D
D. 3 D

Answer

To solve the problem, we need to determine the power of the corrective lens required for a person whose near point is at 0.5 m (50 cm) instead of the normal near point of 25 cm.

### Step-by-Step Solution:

1. **Identify the given values:**
- The near point of the person (D) = 0.5 m = 50 cm
- The normal near point (D') = 25 cm

2. **Use the lens formula:**
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( f \) = focal length of the lens
- \( v \) = image distance (which is taken as -25 cm for the normal near point)
- \( u \) = object distance (which is -50 cm for the person's near point)

3. **Substituting the values into the lens formula:**
\[ \frac{1}{f} = \frac{1}{-25} - \frac{1}{-50} \]

4. **Calculate the right-hand side:**
\[ \frac{1}{f} = -\frac{1}{25} + \frac{1}{50} \]
To combine these fractions, find a common denominator (which is 50):
\[ \frac{1}{f} = -\frac{2}{50} + \frac{1}{50} = -\frac{1}{50} \]

5. **Finding the focal length (f):**
\[ f = -50 \text{ cm} \]

6. **Calculate the power of the lens (P):**
The power of a lens is given by the formula:
\[ P = \frac{1}{f(\text{in meters})} \]
First, convert the focal length from cm to meters:
\[ f = -0.5 \text{ m} \]
Now substitute into the power formula:
\[ P = \frac{1}{-0.5} = -2 \text{ diopters} \]

### Final Answer:
The power of the corrective lens required is **-2 diopters**.

---