A beam of menochromatic blue light of wavelength 4200 Ål in air travels in water of refractive index 4/3. its wavelength in water will be

Options

A. `4200 Å`
B. `5800 Å`
C. `4150 Å`
D. `3150 Å`

Answer

To find the wavelength of monochromatic blue light in water, 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 light in air (\( \lambda_1 \)): 4200 Å (angstroms)
- Refractive index of water (\( \mu_2 \)): \( \frac{4}{3} \)
- Refractive index of air (\( \mu_1 \)): 1 (approximately)

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:
\[ \frac{\lambda_1}{\lambda_2} = \frac{\mu_2}{\mu_1} \]
Rearranging this gives:
\[ \lambda_2 = \lambda_1 \times \frac{\mu_1}{\mu_2} \]

3. **Substitute the Known Values:**
Substitute \( \lambda_1 = 4200 \) Å, \( \mu_1 = 1 \), and \( \mu_2 = \frac{4}{3} \):
\[ \lambda_2 = 4200 \times \frac{1}{\frac{4}{3}} = 4200 \times \frac{3}{4} \]

4. **Calculate \( \lambda_2 \):**
\[ \lambda_2 = 4200 \times \frac{3}{4} = 4200 \times 0.75 = 3150 \text{ Å} \]

5. **Conclusion:**
The wavelength of the monochromatic blue light in water is \( \lambda_2 = 3150 \) Å.

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

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