A person can see clearly only upto a distance of `25 cm`. He wants to read a book placed at a distance of `50cm`. What kind of lens does he require for his spectacles and what must be its power ?

Options

A. Concave, -1.0 D
B. Convex, + 1.5 D
C. Concave, -2.0 D
D. Convex, + 2.0 D

Answer

To solve the problem, we need to determine the type of lens required for a person who can only see clearly up to a distance of 25 cm and wants to read a book placed at a distance of 50 cm.

### Step-by-step Solution:

1. **Identify the Condition**:
The person can see clearly only up to 25 cm, which indicates that he is suffering from myopia (nearsightedness). Myopia means that the person can see nearby objects clearly but has difficulty seeing distant objects.

**Hint**: Myopia is characterized by the inability to see distant objects clearly.

2. **Determine the Object and Image Distances**:
- The object distance (U) is the distance of the book from the person, which is -50 cm (the negative sign indicates that the object is in front of the lens).
- The image distance (V) is the distance at which the person can see clearly, which is -25 cm (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:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
Substituting the values:
\[ \frac{1}{F} = \frac{1}{-25} - \frac{1}{-50} \]

4. **Calculate the Right-Hand Side**:
- Find a common denominator for the fractions:
\[ \frac{1}{-25} = -\frac{2}{50} \]
Thus, we have:
\[ \frac{1}{F} = -\frac{2}{50} + \frac{1}{50} = -\frac{1}{50} \]

5. **Find the Focal Length (F)**:
Taking the reciprocal gives:
\[ F = -50 \text{ cm} \]

6. **Calculate the Power of the Lens**:
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{F \text{ (in meters)}} \]
Converting the focal length from centimeters to meters:
\[ F = -50 \text{ cm} = -0.5 \text{ m} \]
Therefore,
\[ P = \frac{1}{-0.5} = -2 \text{ diopters} \]

7. **Conclusion**:
The person requires a concave lens for his spectacles with a power of -2 diopters.

### Final Answer:
The person requires a concave lens with a power of -2 diopters.