The refactive index of diamond and a glass slab is 2.47 and 1.68, respectively. Determine the ratio of speed of light in diamond and glass slab.

Answer

To determine the ratio of the speed of light in diamond and glass, we can use the relationship between the refractive index and the speed of light in different media.

### Step-by-Step Solution:

1. **Understand the Refractive Index**:
The refractive index (μ) 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). Mathematically, this is expressed as:
\[ \mu = \frac{C}{V} \]

2. **Identify Given Values**:
- The refractive index of diamond (μ_d) = 2.47
- The refractive index of glass (μ_g) = 1.68

3. **Set Up the Ratio of Speeds**:
From the definition of refractive index, we can express the speed of light in diamond (V_d) and glass (V_g) as:
\[ V_d = \frac{C}{\mu_d} \quad \text{and} \quad V_g = \frac{C}{\mu_g} \]

4. **Calculate the Ratio of Speeds**:
To find the ratio of the speed of light in diamond to that in glass, we can write:
\[ \frac{V_d}{V_g} = \frac{\frac{C}{\mu_d}}{\frac{C}{\mu_g}} = \frac{\mu_g}{\mu_d} \]

5. **Substitute the Values**:
Now, substituting the values of the refractive indices:
\[ \frac{V_d}{V_g} = \frac{1.68}{2.47} \]

6. **Perform the Calculation**:
Now, we can calculate the ratio:
\[ \frac{V_d}{V_g} \approx 0.68 \]

### Final Answer:
The ratio of the speed of light in diamond to the speed of light in glass is approximately 0.68.

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