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 solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understand 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 is the dispersion of light into its constituent colors. To achieve this, the two lenses must have different refractive indices and dispersive powers. If the materials were the same, they would not effectively cancel out the chromatic aberration.

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

**Explanation**:
For an achromatic doublet, the dispersive powers must indeed be such that they can counteract each other. This means that if one lens has a positive dispersive power, the other must have a negative dispersive power to ensure that the overall system does not disperse light into its constituent colors.

### Step 3: Analyze the Relationship Between A and R
Now we need to determine if the assertion and reason are true or false and if they are related.

- **Assertion (A)**: True. The materials of the two lenses must be different to form an achromatic doublet.
- **Reason (R)**: True. The dispersive powers must be of opposite signs to achieve the desired effect.

### Conclusion
Since both the assertion and the reason are true, but the reason does not directly explain the assertion (the assertion is about the materials being different, while the reason is about the dispersive powers), we conclude that:

- Assertion (A) is true.
- Reason (R) is true, but it does not explain the assertion.

### Final Answer
The correct option is that the assertion is true, and the reason is also true, but the reason does not explain the assertion.

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