Two lenses of power 15D and -3D are placed in contact. The focal length of the combination is a

Options

A. 10cm
B. 15cm
C. 12cm
D. 18cm

Explanation

To find the focal length of the combination of two lenses with powers of +15D and -3D, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Powers of the Lenses:**
- Let \( P_1 = +15D \) (power of the first lens)
- Let \( P_2 = -3D \) (power of the second lens)

2. **Calculate the Total Power of the Combination:**
- The total power \( P_c \) of the combination of lenses in contact is given by:
\[ P_c = P_1 + P_2 \]
- Substituting the values:
\[ P_c = 15D + (-3D) = 15D - 3D = 12D \]

3. **Relate Power to Focal Length:**
- The relationship between power \( P \) and focal length \( f \) is given by:
\[ P = \frac{1}{f} \]
- Therefore, we can express the focal length of the combination as:
\[ f_c = \frac{1}{P_c} \]

4. **Calculate the Focal Length:**
- Substituting the total power into the formula:
\[ f_c = \frac{1}{12D} \]
- Since the power is in diopters, the focal length will be in meters:
\[ f_c = \frac{1}{12} \text{ meters} = 0.0833 \text{ meters} \]

5. **Convert Focal Length to Centimeters:**
- To convert meters to centimeters, multiply by 100:
\[ f_c = 0.0833 \times 100 = 8.33 \text{ cm} \]

6. **Final Answer:**
- The focal length of the combination of the two lenses is approximately:
\[ f_c \approx 8 \text{ cm} \]