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. 9 D
B. 2 D
C. 3 D
D. 7 D

Explanation

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

### Step 1: Understand the relationship between focal length and power
The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length of the lens in meters.

### Step 2: Convert the focal lengths to meters
The given focal lengths are:
- \( f_1 = 20 \, \text{cm} = 0.20 \, \text{m} \)
- \( f_2 = 25 \, \text{cm} = 0.25 \, \text{m} \)

### Step 3: Calculate the power of each lens
Using the formula for power:
- For lens 1:
\[ P_1 = \frac{1}{f_1} = \frac{1}{0.20} = 5 \, \text{diopters} \]

- For lens 2:
\[ P_2 = \frac{1}{f_2} = \frac{1}{0.25} = 4 \, \text{diopters} \]

### Step 4: Calculate the effective power of the combination
When two lenses are placed in contact, the effective power \( P \) of the combination is the sum of the individual powers:
\[ P = P_1 + P_2 \]
Substituting the values we calculated:
\[ P = 5 + 4 = 9 \, \text{diopters} \]

### Conclusion
The effective power of the combination of the two lenses is \( 9 \, \text{diopters} \).

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