The refractive index of diamond is `2.47` and that of glass is `1.51`. How much faster does light travel in glass than in diamond ?

Explanation

To find out how much faster light travels in glass than in diamond, we can use the relationship between the speed of light in a medium and its refractive index.

### Step-by-Step Solution:

1. **Understand the relationship between speed of light and refractive index**:
The speed of light in a medium (v) is given by the formula:
\[ v = \frac{c}{n} \]
where \(c\) is the speed of light in vacuum (approximately \(3 \times 10^8 \, m/s\)), and \(n\) is the refractive index of the medium.

2. **Calculate the speed of light in diamond**:
Given the refractive index of diamond \(n_{diamond} = 2.47\):
\[ v_{diamond} = \frac{c}{n_{diamond}} = \frac{3 \times 10^8 \, m/s}{2.47} \]

3. **Calculate the speed of light in glass**:
Given the refractive index of glass \(n_{glass} = 1.51\):
\[ v_{glass} = \frac{c}{n_{glass}} = \frac{3 \times 10^8 \, m/s}{1.51} \]

4. **Find the ratio of the speeds**:
To find how much faster light travels in glass than in diamond, we calculate the ratio:
\[ \text{Ratio} = \frac{v_{glass}}{v_{diamond}} = \frac{\frac{c}{n_{glass}}}{\frac{c}{n_{diamond}}} = \frac{n_{diamond}}{n_{glass}} \]

5. **Substitute the values of the refractive indices**:
\[ \text{Ratio} = \frac{2.47}{1.51} \]

6. **Calculate the numerical value**:
\[ \text{Ratio} \approx 1.635 \]

7. **Conclusion**:
This means that light travels approximately \(1.635\) times faster in glass than in diamond.