The index of refraction of flised quartz is 1.472 for light of wavelength 400 nm and is 1.452 for light of wavelength 760 nm. Find the speeds of light of these wavelengths in fused quartz.

Explanation

To solve the problem of finding the speeds of light of different wavelengths in fused quartz, we will use the relationship between the refractive index and the speed of light. The refractive index (μ) is defined as the ratio of the speed of light in a vacuum (or air) (c) to the speed of light in the medium (v):

\[ \mu = \frac{c}{v} \]

Where:
- \( c \) is the speed of light in air (approximately \( 3 \times 10^8 \) m/s).
- \( v \) is the speed of light in the medium (fused quartz in this case).

### Step 1: Calculate the speed of light for the wavelength of 400 nm

1. **Identify the refractive index for 400 nm**:
- Given \( \mu_1 = 1.472 \).

2. **Use the formula to find the speed of light in fused quartz (V1)**:
\[ V_1 = \frac{c}{\mu_1} \]
Substituting the values:
\[ V_1 = \frac{3 \times 10^8 \, \text{m/s}}{1.472} \]

3. **Calculate \( V_1 \)**:
\[ V_1 \approx 2.04 \times 10^8 \, \text{m/s} \]

### Step 2: Calculate the speed of light for the wavelength of 760 nm

1. **Identify the refractive index for 760 nm**:
- Given \( \mu_2 = 1.452 \).

2. **Use the formula to find the speed of light in fused quartz (V2)**:
\[ V_2 = \frac{c}{\mu_2} \]
Substituting the values:
\[ V_2 = \frac{3 \times 10^8 \, \text{m/s}}{1.452} \]

3. **Calculate \( V_2 \)**:
\[ V_2 \approx 2.07 \times 10^8 \, \text{m/s} \]

### Final Answers:
- The speed of light in fused quartz for 400 nm wavelength is approximately \( 2.04 \times 10^8 \, \text{m/s} \).
- The speed of light in fused quartz for 760 nm wavelength is approximately \( 2.07 \times 10^8 \, \text{m/s} \).

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