The near point of a person is 75 cm. In order that he may be able to read book at a distance 30 cm. The power of spectacles lenses should be

Options

A. `-2D`
B. `+3.75D`
C. `+2D`
D. `+3D`

Answer

To solve the problem, we need to determine the power of the spectacles required for a person whose near point is 75 cm, so that they can read a book at a distance of 30 cm.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- The near point of the person (the closest distance at which they can see clearly) is given as \( D = 75 \, \text{cm} \).
- The object distance (the distance at which the person wants to read) is \( u = -30 \, \text{cm} \) (negative because the object is on the same side as the incoming light).

2. **Using the Lens Formula**:
- The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
- Here, \( v \) is the image distance, which will be equal to the near point of the person, so \( v = -75 \, \text{cm} \).

3. **Substituting Values into the Lens Formula**:
- Substitute \( v = -75 \, \text{cm} \) and \( u = -30 \, \text{cm} \) into the lens formula:
\[ \frac{1}{f} = \frac{1}{-75} - \frac{1}{-30} \]

4. **Calculating the Right-Hand Side**:
- Finding a common denominator (which is 150):
\[ \frac{1}{f} = \frac{-2}{150} + \frac{5}{150} = \frac{3}{150} \]
- Thus,
\[ \frac{1}{f} = \frac{1}{50} \]

5. **Finding the Focal Length**:
- From the above equation, we can find the focal length \( f \):
\[ f = 50 \, \text{cm} \]

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

7. **Conclusion**:
- The power of the spectacles required is \( +2 \, \text{D} \).

### Final Answer:
The power of the spectacles lenses should be \( +2 \, \text{D} \).

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