A far sighted person cannot see object clearly al a distance less than 75 cm from his eyes. The power of the lens needed to read an object al 25 cm is

Options

A. `+1.50 D`
B. `+2.67 D`
C. `-2.67 d`
D. `-1.50 d`

Answer

To solve the problem of determining the power of the lens needed for a farsighted person to read an object at 25 cm, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Condition of the Person**:
- The person is farsighted (hypermetropia) and cannot see objects clearly closer than 75 cm. This means the least distance of distinct vision (D) for this person is 75 cm.

2. **Identify the Object and Image Distances**:
- The object distance (U) for reading is given as 25 cm. Since the object is placed on the same side as the incoming light, we take U as negative:
\[ U = -25 \text{ cm} \]
- The image distance (V) where the person can see clearly is 75 cm (the minimum distance at which the person can see clearly):
\[ V = -75 \text{ cm} \]

3. **Use the Lens Formula**:
- The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
- Substituting the values of U and V into the lens formula:
\[ \frac{1}{F} = \frac{1}{-75} - \frac{1}{-25} \]

4. **Calculate the Right-Hand Side**:
- To find a common denominator (which is 75), we rewrite the fractions:
\[ \frac{1}{F} = -\frac{1}{75} + \frac{3}{75} = \frac{2}{75} \]

5. **Find the Focal Length (F)**:
- Now, take the reciprocal to find F:
\[ F = \frac{75}{2} = 37.5 \text{ cm} \]

6. **Convert Focal Length to Meters**:
- Convert the focal length from centimeters to meters:
\[ F = 0.375 \text{ m} \]

7. **Calculate the Power of the Lens (P)**:
- The power of a lens is given by:
\[ P = \frac{1}{F} \text{ (in meters)} \]
- Substituting the value of F:
\[ P = \frac{1}{0.375} \approx 2.67 \text{ diopters} \]

8. **Determine the Type of Lens**:
- Since the power is positive, it indicates that a convex lens is needed for correction.

### Final Answer:
The power of the lens needed for the farsighted person to read an object at 25 cm is approximately **+2.67 diopters**.

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