STATEMENT-1: A lens has two principal focal lengths which may be different in magnitude. STATEMENT-2: The distance of both principal focus from optical centre of lens depend on the two radii of curvature of the lens. Distance of both principal focus from optical centre a lens are same only if radii of curvature of both sides of lens are same

Options

A. Statement-1 is true, Statement-2: is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is true, Statement-2: is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is true but statement-2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To analyze the two statements provided in the question, we will evaluate each one step by step.

### Step 1: Evaluate Statement 1
**Statement 1:** A lens has two principal focal lengths which may be different in magnitude.

- **Explanation:** This statement is true. A lens, particularly a double convex or double concave lens, is formed by two surfaces that can have different curvatures. Since the focal length of a lens is dependent on the curvature of its surfaces, it is possible for the two principal focal lengths to differ in magnitude.

### Step 2: Evaluate Statement 2
**Statement 2:** The distance of both principal focus from the optical centre of the lens depends on the two radii of curvature of the lens. The distance of both principal focus from the optical centre of a lens is the same only if the radii of curvature of both sides of the lens are the same.

- **Explanation:** This statement is partially true but ultimately false due to the use of the word "only." The distance of the principal foci does depend on the radii of curvature, but it also depends on the refractive index of the lens material, as described by the lens maker's formula:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]
Here, \(f\) is the focal length, \(\mu\) is the refractive index, and \(r_1\) and \(r_2\) are the radii of curvature. Therefore, the statement is false because it implies that the radii of curvature alone determine the focal lengths without considering the material's refractive index.

### Conclusion
- **Final Evaluation:**
- Statement 1 is true.
- Statement 2 is false due to the misleading use of the word "only."

### Answer
The correct option is that Statement 1 is true, but Statement 2 is false.

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