Two thin lenses of focal lengths 20 cm and 25 cm are placed in a contact. The effective power of the combination is

Options

A. 10 D
B. 9 D
C. 8 D
D. 5 D

Answer

To find the effective power of two thin lenses placed in contact, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Focal Lengths**:
- The focal length of the first lens, \( f_1 = 20 \, \text{cm} \).
- The focal length of the second lens, \( f_2 = 25 \, \text{cm} \).

2. **Convert Focal Lengths to Meters**:
- Since power is measured in diopters (D), we need to convert the focal lengths from centimeters to meters:
\[ f_1 = 20 \, \text{cm} = 0.20 \, \text{m} \]
\[ f_2 = 25 \, \text{cm} = 0.25 \, \text{m} \]

3. **Calculate the Power of Each Lens**:
- The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{f} \quad \text{(where } f \text{ is in meters)} \]
- Therefore, the power of the first lens \( P_1 \) is:
\[ P_1 = \frac{1}{f_1} = \frac{1}{0.20} = 5 \, \text{D} \]
- The power of the second lens \( P_2 \) is:
\[ P_2 = \frac{1}{f_2} = \frac{1}{0.25} = 4 \, \text{D} \]

4. **Calculate the Effective Power of the Combination**:
- When two lenses are placed in contact, the effective power \( P_E \) is the sum of the individual powers:
\[ P_E = P_1 + P_2 \]
- Substituting the values we calculated:
\[ P_E = 5 + 4 = 9 \, \text{D} \]

5. **Final Result**:
- The effective power of the combination of the two lenses is:
\[ P_E = 9 \, \text{D} \]