Two lenses of power`+2.50D`and`-3.75D`are combined to form a compound lens Its focal length in cm,will be

Options

A. 40
B. -40
C. -80
D. 160

Explanation

To find the focal length of the compound lens formed by combining two lenses with powers of +2.50 D and -3.75 D, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Powers of the Lenses**:
- The first lens has a power \( P_1 = +2.50 \, D \) (convex lens).
- The second lens has a power \( P_2 = -3.75 \, D \) (concave lens).

2. **Calculate the Total Power of the Compound Lens**:
- The total power \( P \) of the combined lenses is given by the sum of their individual powers:
\[ P = P_1 + P_2 = 2.50 + (-3.75) = 2.50 - 3.75 = -1.25 \, D \]

3. **Calculate the Focal Length of the Compound Lens**:
- The relationship between power \( P \) and focal length \( f \) is given by:
\[ P = \frac{1}{f} \]
- Rearranging this formula gives:
\[ f = \frac{1}{P} \]
- Substituting the value of \( P \):
\[ f = \frac{1}{-1.25} = -0.8 \, \text{meters} \]

4. **Convert Focal Length to Centimeters**:
- Since \( 1 \, \text{meter} = 100 \, \text{centimeters} \), we convert the focal length:
\[ f = -0.8 \, \text{meters} \times 100 = -80 \, \text{centimeters} \]

5. **Conclusion**:
- The focal length of the compound lens is \( -80 \, \text{cm} \).

### Final Answer:
The focal length of the compound lens is **-80 cm**.

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