Statement-I : Sun glasses have zero power even through their surfaces are curved.
and
Statement-II: Both surface of the sun glasses are curved in the same direction with same radii.

Options

A. Statement-I is true , Statement -II is true, Statement-II is correct explanation for Statement-I.
B. Statement - I is true, Statement -II is true: Statement -II is NOT a correct explanation for statement -I .
C. Statement-I is true, Statement-II is false.
D. statement-I is false, statement- II is true.

Answer

To solve the question, we need to analyze both statements regarding the sunglasses and their optical properties.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- Statement I claims that sunglasses have zero power despite their surfaces being curved.
- Power (P) of a lens is defined as the reciprocal of its focal length (F), given by the formula:
\[ P = \frac{1}{F} \]
- If the power is zero, it implies that the focal length is infinite (F = ∞).

2. **Understanding Statement II**:
- Statement II states that both surfaces of the sunglasses are curved in the same direction with the same radii.
- For a lens, the lens maker's formula is given by:
\[ \frac{1}{F} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
- Here, \( n \) is the refractive index of the lens material, and \( R_1 \) and \( R_2 \) are the radii of curvature of the two surfaces.

3. **Analyzing the Lens Maker's Formula**:
- Since both surfaces are curved in the same direction and have the same radius of curvature, we can denote:
\[ R_1 = R \quad \text{and} \quad R_2 = R \]
- Therefore, substituting into the lens maker's formula:
\[ \frac{1}{F} = (n - 1) \left( \frac{1}{R} - \frac{1}{R} \right) = (n - 1) \cdot 0 = 0 \]
- This implies that \( \frac{1}{F} = 0 \), hence \( F = \infty \).

4. **Conclusion**:
- Since the focal length is infinite, the power of the sunglasses is indeed zero.
- Therefore, both statements are true, and Statement II correctly explains Statement I.

### Final Answer:
Both Statement I and Statement II are true, and Statement II provides the correct explanation for Statement I.

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