The wavelength of sodium light in air is 5890 Å . The velocity of light in air is `3xx10^(8) ms^(-1)`. The wavelength of light in a glass of refractive index 1.6 would be close to

Options

A. 5890 Å
B. 3681 Å
C. 9424 Å
D. 15078 Å

Answer

To find the wavelength of sodium light in glass, we can use the relationship between the wavelength of light in different media and the refractive index.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Wavelength of sodium light in air, \( \lambda_1 = 5890 \, \text{Å} \)
- Refractive index of glass, \( n = 1.6 \)
- Velocity of light in air, \( c = 3 \times 10^8 \, \text{m/s} \)

2. **Use the Relationship Between Wavelength and Refractive Index:**
The relationship between the wavelength in air (\( \lambda_1 \)) and the wavelength in glass (\( \lambda_2 \)) is given by:
\[ \frac{\lambda_2}{\lambda_1} = \frac{1}{n} \]
Rearranging gives:
\[ \lambda_2 = \lambda_1 \cdot \frac{1}{n} \]

3. **Substitute the Values:**
Substitute the known values into the equation:
\[ \lambda_2 = 5890 \, \text{Å} \cdot \frac{1}{1.6} \]

4. **Calculate \( \lambda_2 \):**
\[ \lambda_2 = \frac{5890}{1.6} \approx 3681.25 \, \text{Å} \]

5. **Round the Result:**
The wavelength of light in glass can be approximated as:
\[ \lambda_2 \approx 3681 \, \text{Å} \]

### Final Answer:
The wavelength of sodium light in glass of refractive index 1.6 is approximately **3681 Å**.

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