A : When two lenses in contact form an achromatic doublet, then the materials of the two lenses are always different.
R : The dispersive powers of the materials of the two lenses are of opposite sign.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To determine the correctness of the assertion (A) and reason (R) regarding the formation of an achromatic doublet, we can analyze both statements step by step.

### Step 1: Understanding the Assertion (A)
The assertion states that when two lenses in contact form an achromatic doublet, the materials of the two lenses are always different.

- **Explanation**: An achromatic doublet is designed to minimize chromatic aberration, which occurs due to the different refractive indices for different wavelengths of light. To achieve this, the two lenses must have different refractive indices, which implies that they must be made from different materials. Thus, the assertion is correct.

### Step 2: Understanding the Reason (R)
The reason states that the dispersive powers of the materials of the two lenses are of opposite sign.

- **Explanation**: Dispersive power refers to how much a material can spread out different wavelengths of light. For an achromatic doublet to effectively cancel out chromatic aberration, one lens must have a positive dispersive power and the other must have a negative dispersive power. This means that the materials must indeed have dispersive powers of opposite signs to achieve the desired effect. Thus, the reason is also correct.

### Conclusion
Both the assertion (A) and the reason (R) are correct, and the reason provides a valid explanation for the assertion.

### Final Answer
- **Assertion (A)**: True
- **Reason (R)**: True
- **Explanation**: The materials of the two lenses are different to achieve an achromatic doublet, and their dispersive powers must be of opposite signs to effectively cancel chromatic aberration.

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