A longsighted person has a minimum distance of distinct vision of 50 cm. He wants to reduce it to 25 cm. He should use a

Options

A. concavelens of focal length 50 cm
B. Convex lens of focal length 25 cm
C. Convex lens of focal length 50 cm
D. Convave lens of focal length 25 cm

Answer

To solve the problem of a longsighted person who wants to reduce his minimum distance of distinct vision from 50 cm to 25 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- The person has a minimum distance of distinct vision (D) of 50 cm. This means he can only see objects clearly that are at least 50 cm away.
- He wants to reduce this distance to 25 cm.

2. **Identify the Lens Type**:
- A longsighted person (hypermetropic) requires a convex lens to help them see nearby objects clearly.

3. **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
- \( u \) = object distance

4. **Set the Object and Image Distances**:
- For the person to see an object at 25 cm clearly, we need to set the image distance \( v \) to -25 cm (the negative sign indicates that the image is virtual and on the same side as the object).
- Since the person can see objects clearly at 50 cm, we set the object distance \( u \) to -50 cm (the object is also on the same side).

5. **Substitute Values into the Lens Formula**:
- Substitute \( v = -25 \) cm and \( u = -50 \) cm into the lens formula:
\[ \frac{1}{f} = \frac{1}{-25} - \frac{1}{-50} \]

6. **Calculate the Focal Length**:
- Calculate the right side:
\[ \frac{1}{f} = -\frac{1}{25} + \frac{1}{50} \]
- Finding a common denominator (50):
\[ \frac{1}{f} = -\frac{2}{50} + \frac{1}{50} = -\frac{1}{50} \]
- Therefore, \( f = -50 \) cm.

7. **Determine the Type of Lens**:
- Since the focal length is negative, this indicates that the lens needed is a concave lens.

8. **Conclusion**:
- The person should use a concave lens with a focal length of 50 cm to reduce his minimum distance of distinct vision to 25 cm.

### Final Answer:
The person should use a concave lens of focal length 50 cm.