A beam of monochromatic light is refracted from vacuum into a medium of refractive index `1.5` The wavelength of refracted light will be

Options

A. dependent on intensity of refracted light
B. same
C. smaller
D. large

Answer

To solve the problem of finding the wavelength of light refracted from vacuum into a medium with a refractive index of 1.5, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a beam of monochromatic light (which means it has a single wavelength) that is traveling from vacuum into a medium with a refractive index (μ) of 1.5.

2. **Refractive Index Definition**:
- The refractive index (μ) is defined as the ratio of the speed of light in vacuum (C) to the speed of light in the medium (V):
\[ \mu = \frac{C}{V} \]
- Here, \(C\) is approximately \(3 \times 10^8 \, \text{m/s}\).

3. **Relationship Between Wavelength and Refractive Index**:
- When light travels from one medium to another, its frequency (ν) remains constant, but its speed and wavelength change. The relationship can be expressed as:
\[ V = \lambda \cdot \nu \]
- Therefore, when light enters a medium with a refractive index, the new wavelength (λ') in the medium can be calculated using:
\[ \lambda' = \frac{\lambda}{\mu} \]
- Here, λ is the original wavelength in vacuum.

4. **Calculating the New Wavelength**:
- Given that the refractive index (μ) is 1.5, we can substitute this into our equation:
\[ \lambda' = \frac{\lambda}{1.5} \]
- This shows that the wavelength in the medium will be smaller than the wavelength in vacuum.

5. **Conclusion**:
- The wavelength of the refracted light will be \( \frac{\lambda}{1.5} \).

### Final Answer:
- The wavelength of the refracted light in the medium is \( \frac{\lambda}{1.5} \).