Two lens of power - 12D and + 7D are in contact with each other, the focal length of combination is :

Options

A. 10 cm
B. - 20 cm
C. - 10 cm
D. 20 cm

Answer

To find the focal length of the combination of two lenses in contact, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Powers of the Lenses**:
- The power of the first lens (P1) is -12 D (diopters).
- The power of the second lens (P2) is +7 D.

2. **Calculate the Total Power of the Combination**:
- When two lenses are in contact, the total power (P) is the sum of their individual powers:
\[ P = P1 + P2 \]
- Substituting the values:
\[ P = -12 D + 7 D = -5 D \]

3. **Relate Power to Focal Length**:
- The relationship between power (P) and focal length (f) is given by:
\[ P = \frac{1}{f} \]
- Rearranging this equation to find the focal length:
\[ f = \frac{1}{P} \]

4. **Calculate the Focal Length**:
- Substitute the total power into the equation:
\[ f = \frac{1}{-5 D} \]
- This gives:
\[ f = -0.2 \text{ meters} \]

5. **Convert Focal Length to Centimeters**:
- Since 1 meter = 100 centimeters, we convert:
\[ f = -0.2 \text{ m} = -20 \text{ cm} \]

### Final Answer:
The focal length of the combination of the two lenses is **-20 cm**.

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