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 determine how much faster light travels in glass than in diamond, we can use the relationship between the speed of light in different media and their respective refractive indices. Here’s a step-by-step solution:

### Step 1: Understand the relationship between refractive index and speed of light
The refractive index (μ) of a medium is defined as:
\[ \mu = \frac{c}{v} \]
where:
- \(c\) is the speed of light in vacuum (approximately \(3 \times 10^8\) m/s),
- \(v\) is the speed of light in the medium.

### Step 2: Write the equations for diamond and glass
For diamond (D):
\[ \mu_D = \frac{c}{v_D} \]
For glass (G):
\[ \mu_G = \frac{c}{v_G} \]

### Step 3: Rearranging the equations to find speeds
From the above equations, we can express the speeds of light in diamond and glass:
\[ v_D = \frac{c}{\mu_D} \]
\[ v_G = \frac{c}{\mu_G} \]

### Step 4: Find the ratio of the speeds
To find how much faster light travels in glass than in diamond, we need to find the ratio \( \frac{v_G}{v_D} \):
\[ \frac{v_G}{v_D} = \frac{\frac{c}{\mu_G}}{\frac{c}{\mu_D}} = \frac{\mu_D}{\mu_G} \]

### Step 5: Substitute the values of refractive indices
Given:
- Refractive index of diamond, \( \mu_D = 2.47 \)
- Refractive index of glass, \( \mu_G = 1.51 \)

Now substituting these values into the ratio:
\[ \frac{v_G}{v_D} = \frac{\mu_D}{\mu_G} = \frac{2.47}{1.51} \]

### Step 6: Calculate the ratio
Calculating the above expression:
\[ \frac{v_G}{v_D} \approx 1.635 \]

### Conclusion
This means that light travels approximately **1.635 times faster in glass than in diamond**.

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