A : Proper cutting of diamond makes it sparkle.
R : Diamond has very large refractive index.

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:

**Assertion (A)**: Proper cutting of diamond makes it sparkle.
**Reason (R)**: Diamond has a very large refractive index.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that proper cutting of diamond makes it sparkle. This is true because the way a diamond is cut affects how light interacts with it. A well-cut diamond has facets that reflect and refract light in such a way that it creates a sparkling effect.

**Hint**: Consider how light behaves when it hits different surfaces of the diamond.

2. **Understanding the Reason**:
The reason states that diamond has a very large refractive index. This is also true. The refractive index (n) of diamond is approximately 2.42, which is significantly higher than that of many other materials. A high refractive index means that light travels slower in diamond compared to air, leading to greater bending of light rays.

**Hint**: Recall the formula for refractive index and how it relates to the speed of light in different media.

3. **Total Internal Reflection**:
Due to the high refractive index of diamond, the critical angle for total internal reflection is very low. The critical angle (C) can be calculated using the formula:
\[ \sin C = \frac{1}{n} \]
For diamond, since n is large, C will be small, allowing light rays that hit the diamond at angles greater than this critical angle to be totally internally reflected.

**Hint**: Think about how total internal reflection contributes to the sparkle of the diamond.

4. **Conclusion**:
Since both the assertion and reason are true, and the reason explains why the assertion is true (the high refractive index allows for total internal reflection, which contributes to the sparkle), we conclude that both statements are correct.

**Final Answer**: Both assertion and reason are true, and the reason is the correct explanation of the assertion.

### Summary of the Answer:
- **Assertion (A)**: True
- **Reason (R)**: True
- **Conclusion**: Both A and R are true, and R is the correct explanation of A.