Which of the following statements is true?

Options

A. A convex lens has 4 dioptre power having a focal length 0.25 m
B. A convex lens has 4 dioptre power having a focal length -0.25 m
C. A concave lens has 4 dioptre power having a focal length 0.25 m
D. A concave lens has 4 dioptre power having a focal length -0.25 m

Explanation

To determine which of the given statements is true, we will analyze each option based on the properties of lenses and the formula for power.

### Step-by-Step Solution:

1. **Understanding the Power of a Lens**:
The power (P) of a lens is defined as the reciprocal of its focal length (f) in meters. The formula is:
\[ P = \frac{1}{f} \]
where:
- P is the power in diopters (D),
- f is the focal length in meters.

2. **Analyzing Option A**:
- Statement: "A convex lens has 4 diopter power having a focal length of 0.25 meters."
- Calculation:
\[ P = \frac{1}{f} = \frac{1}{0.25} = 4 \text{ D} \]
- Since a convex lens has a positive focal length, this statement is **true**.

3. **Analyzing Option B**:
- Statement: "A convex lens has a focal length of -0.25 meters."
- A convex lens cannot have a negative focal length; it must be positive. Therefore, this statement is **false**.

4. **Analyzing Option C**:
- Statement: "A concave lens has 4 diopter power having a focal length of 0.25 meters."
- For a concave lens, the focal length is negative. Thus, if the power is 4 D, the focal length should be:
\[ P = \frac{1}{f} \Rightarrow f = \frac{1}{4} = 0.25 \text{ m (positive)} \]
- This contradicts the property of a concave lens, so this statement is **false**.

5. **Analyzing Option D**:
- Statement: "A concave lens has 4 diopter power having a focal length of -0.25 meters."
- Calculation:
\[ P = \frac{1}{f} = \frac{1}{-0.25} = -4 \text{ D} \]
- The power of a concave lens is negative, so this statement is also **false**.

### Conclusion:
The only true statement is **Option A**: "A convex lens has 4 diopter power having a focal length of 0.25 meters."

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