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 the combination of two thin lenses placed in contact, we can follow these steps:

### Step 1: Identify the focal lengths of the lenses
The focal lengths given are:
- \( f_1 = 20 \, \text{cm} \)
- \( f_2 = 25 \, \text{cm} \)

### Step 2: Convert the focal lengths from centimeters to meters
Since the power is calculated using the focal lengths in meters, we convert:
- \( f_1 = 20 \, \text{cm} = 0.20 \, \text{m} \)
- \( f_2 = 25 \, \text{cm} = 0.25 \, \text{m} \)

### Step 3: Calculate the power of each lens
The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length in meters.

Calculating the power of each lens:
- For the first lens:
\[ P_1 = \frac{1}{f_1} = \frac{1}{0.20} = 5 \, \text{D} \]
- For the second lens:
\[ P_2 = \frac{1}{f_2} = \frac{1}{0.25} = 4 \, \text{D} \]

### Step 4: Calculate the effective power of the combination
The effective power \( P_{\text{effective}} \) of the combination of lenses in contact is the sum of their individual powers:
\[ P_{\text{effective}} = P_1 + P_2 \]
Substituting the values we calculated:
\[ P_{\text{effective}} = 5 + 4 = 9 \, \text{D} \]

### Step 5: State the final answer
The effective power of the combination of the two lenses is:
\[ \boxed{9 \, \text{D}} \]

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