A beam of monochromatic blue light of wavelength 4200 Å in air travels in water `(mu = 4//3)`. It's wavelengths in water will be

Options

A. 2800 Å
B. 5600 Å
C. 3150 Å
D. 4000 Å

Explanation

To find the wavelength of monochromatic blue light in water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Wavelength of blue light in air, \( \lambda_{\text{air}} = 4200 \, \text{Å} \)
- Refractive index of water, \( \mu = \frac{4}{3} \)

2. **Use the Relationship Between Wavelength and Refractive Index:**
The relationship between the wavelength in air and the wavelength in a medium is given by:
\[ \lambda_{\text{medium}} = \frac{\lambda_{\text{air}}}{\mu} \]
where \( \lambda_{\text{medium}} \) is the wavelength in the medium (water in this case).

3. **Substitute the Values:**
Substitute the known values into the equation:
\[ \lambda_{\text{water}} = \frac{4200 \, \text{Å}}{\frac{4}{3}} \]

4. **Calculate the Wavelength in Water:**
To simplify the calculation:
\[ \lambda_{\text{water}} = 4200 \, \text{Å} \times \frac{3}{4} \]
\[ \lambda_{\text{water}} = 4200 \times 0.75 \]
\[ \lambda_{\text{water}} = 3150 \, \text{Å} \]

5. **Conclusion:**
The wavelength of the monochromatic blue light in water is \( \lambda_{\text{water}} = 3150 \, \text{Å} \).

### Final Answer:
The wavelength of the monochromatic blue light in water is **3150 Å**.

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