Two lenses of power +10 D and -2D are combined together then focal length of combination is

Options

A. `-20cm`
B. `-12.5cm`
C. `12.5cm`
D. `15cm`

Explanation

To find the focal length of the combination of two lenses with given powers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Powers of the Lenses**:
- Let the power of the first lens, \( P_1 = +10 \, D \) (diopters).
- Let the power of the second lens, \( P_2 = -2 \, D \) (diopters).

2. **Calculate the Total Power of the Combination**:
- The total power \( P \) of the combination of lenses is given by the formula:
\[ P = P_1 + P_2 \]
- Substituting the values:
\[ P = 10 \, D + (-2 \, D) = 10 - 2 = 8 \, D \]

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

4. **Calculate the Focal Length**:
- Substituting the total power into the formula:
\[ f = \frac{1}{8 \, D} = 0.125 \, m \]

5. **Convert Focal Length to Centimeters**:
- Since \( 1 \, m = 100 \, cm \), we convert the focal length:
\[ f = 0.125 \, m \times 100 = 12.5 \, cm \]

6. **Conclusion**:
- The focal length of the combination of the two lenses is \( 12.5 \, cm \).

### Final Answer:
The focal length of the combination is \( 12.5 \, cm \).

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