If f is focal length of the lens, then the power of a lens is equal to

Options

A. `100/(f(cm))`
B. `10/(f(cm))`
C. `100/(f(m))`
D. `1/(100f(cm))`

Explanation

To find the power of a lens given its focal length (f), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The power (P) of a lens is defined as the reciprocal of its focal length (f) measured in meters. The formula is:
\[ P = \frac{1}{f} \quad \text{(in meters)} \]

2. **Convert Focal Length to Meters**: If the focal length is given in centimeters, we need to convert it to meters since the power is defined in diopters (D), where 1 D = 1/m. The conversion is:
\[ f \, (\text{in meters}) = \frac{f \, (\text{in cm})}{100} \]

3. **Substitute in the Power Formula**: Now, substituting the converted focal length into the power formula:
\[ P = \frac{1}{\left(\frac{f \, (\text{in cm})}{100}\right)} = \frac{100}{f \, (\text{in cm})} \]

4. **Conclusion**: Therefore, the power of the lens in terms of its focal length in centimeters is:
\[ P = \frac{100}{f \, (\text{in cm})} \]