Power of a lens , `P=(1)/(f)`

Answer

To solve the question regarding the power of a lens, we need to understand the relationship between the power (P) and the focal length (f) of the lens. The formula given is:

\[ P = \frac{1}{f} \]

where:
- \( P \) is the power of the lens,
- \( f \) is the focal length of the lens.

### Step-by-Step Solution:

1. **Understanding the Formula**:
- The formula states that the power of a lens is the reciprocal of its focal length.

2. **Units of Focal Length**:
- The focal length \( f \) must be measured in meters (m) for the formula to be valid.

3. **Calculating Power**:
- To find the power \( P \), you take the reciprocal of the focal length. If \( f \) is given in meters, then:
\[ P = \frac{1}{f} \text{ (in meters)} \]

4. **Units of Power**:
- The unit of power is the diopter (D). Therefore, when you calculate \( P \), the result will be in diopters.

5. **Sign Convention**:
- It is important to note the sign convention:
- For converging lenses, the focal length is positive.
- For diverging lenses, the focal length is negative.

6. **Final Statement**:
- The statement that the power of a lens is given by \( P = \frac{1}{f} \) is correct, provided that the focal length is in meters and the appropriate sign is used.

### Summary:
- The power of a lens is calculated using the formula \( P = \frac{1}{f} \).
- Ensure \( f \) is in meters.
- The unit of power is diopter (D).
- Use the correct sign for the focal length based on the type of lens.