A light ray in passing from water to a medium (a) speeds up, (b) slows down. In each case, (i) give one example of the medium, (ii) state whether the refractive index of medium is equal to, less than or greater than the refractive index of water.

Answer

### Step-by-Step Solution

1. **Understanding the Concept of Refractive Index**:
- The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). It is given by the formula:
\[ n = \frac{c}{v} \]
- The refractive index is inversely related to the speed of light in that medium. This means that if the refractive index increases, the speed of light decreases, and vice versa.

2. **Case (a): Light Ray Speeds Up (from Water to a Medium)**:
- When a light ray moves from water to another medium and speeds up, it indicates that the new medium has a lower refractive index than water.
- The refractive index of water (n_w) is approximately 1.33.
- To find a suitable medium where the refractive index is less than that of water, we can consider **air**, which has a refractive index of about 1.00.
- Therefore, in this case:
- **Example of the Medium**: Air
- **Refractive Index Comparison**: The refractive index of air (n) is less than that of water (n_w).

3. **Case (b): Light Ray Slows Down (from Water to a Medium)**:
- When a light ray moves from water to another medium and slows down, it indicates that the new medium has a higher refractive index than water.
- We need to find a medium with a refractive index greater than 1.33.
- A suitable example is **diamond**, which has a refractive index of approximately 2.42.
- Therefore, in this case:
- **Example of the Medium**: Diamond
- **Refractive Index Comparison**: The refractive index of diamond (n) is greater than that of water (n_w).

### Summary of Answers
- **(a)** Light speeds up:
- Example of medium: Air
- Refractive index: Less than that of water.

- **(b)** Light slows down:
- Example of medium: Diamond
- Refractive index: Greater than that of water.