The least distance of vision of a longsighted person is 60 cm. By using a spectacle lens, this distance is reduced to 12 cm. The power of the lens is

Options

A. `+5.0 D`
B. `+(20/3) D`
C. `–(10/3) D`
D. `+2.0 D`

Explanation

To find the power of the lens required to correct the vision of a longsighted person, we can use the lens formula and the formula for power of a lens.

### Step-by-Step Solution:

1. **Identify the given values**:
- Least distance of vision without lens (D) = 60 cm = 0.6 m
- Least distance of vision with lens (d) = 12 cm = 0.12 m

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 the least distance of vision with lens, d = 0.12 m)
- \( u \) = object distance (which is the least distance of vision without lens, D = -0.6 m, negative because it is on the same side as the object)

3. **Substituting the values**:
\[ \frac{1}{f} = \frac{1}{0.12} - \frac{1}{-0.6} \]

4. **Calculate \( \frac{1}{f} \)**:
\[ \frac{1}{f} = \frac{1}{0.12} + \frac{1}{0.6} \]
- Calculate \( \frac{1}{0.12} = 8.33 \, \text{m}^{-1} \)
- Calculate \( \frac{1}{0.6} = 1.67 \, \text{m}^{-1} \)
\[ \frac{1}{f} = 8.33 + 1.67 = 10 \, \text{m}^{-1} \]

5. **Finding the focal length \( f \)**:
\[ f = \frac{1}{10} = 0.1 \, \text{m} = 10 \, \text{cm} \]

6. **Calculate the power of the lens**:
The power \( P \) of a lens is given by:
\[ P = \frac{1}{f} \text{ (in meters)} \]
\[ P = \frac{1}{0.1} = 10 \, \text{diopters} \]

### Final Answer:
The power of the lens is +10 diopters.