(a) For which colour of white light, is the refractive index of a transparent medium (i) the least, (ii) the most ?
(b) Which colour of light travels fastest in any medium except air ?

Answer

### Step-by-Step Solution

**(a)** To determine the colors of white light for which the refractive index of a transparent medium is the least and the most, we need to understand the relationship between the wavelength of light and the refractive index.

1. **Understanding Wavelength and Refractive Index:**
- The refractive index (n) of a medium is inversely proportional to the wavelength (λ) of light. This means that as the wavelength increases, the refractive index decreases, and vice versa.
- Mathematically, this can be expressed as:
\[ n \propto \frac{1}{\lambda} \]

2. **Identifying Wavelengths of Colors:**
- In the visible spectrum, red light has the longest wavelength (approximately 800 nm or 8000 Å) and violet light has the shortest wavelength (approximately 400 nm or 4000 Å).

3. **Determining the Least Refractive Index:**
- Since red light has the longest wavelength, it will have the least refractive index in a transparent medium.
- **Answer for part (i):** Red light has the least refractive index.

4. **Determining the Most Refractive Index:**
- Conversely, violet light, having the shortest wavelength, will have the highest refractive index.
- **Answer for part (ii):** Violet light has the most refractive index.

**(b)** Now, we need to find out which color of light travels fastest in any medium except air.

1. **Understanding Speed of Light in a Medium:**
- The speed of light (v) in a medium is directly proportional to its wavelength (λ). This means that light with a longer wavelength will travel faster in a medium compared to light with a shorter wavelength.
- Mathematically, this can be expressed as:
\[ v \propto \lambda \]

2. **Identifying the Color with Maximum Wavelength:**
- Since red light has the longest wavelength (800 nm), it will travel the fastest in any medium except air.
- **Answer for part (b):** Red light travels fastest in any medium except air.

### Final Answers
- (a) (i) Red light has the least refractive index. (ii) Violet light has the most refractive index.
- (b) Red light travels fastest in any medium except air.