When a light ray from a rarer medium is refracted into a denser medium, its

Options

A. Speed increases, wavelength increases
B. Speed decreases, wavelength increases
C. Speed increases, wavelength decreases
D. Speed decreases, wavelength decreases

Answer

To solve the question regarding the behavior of a light ray when it moves from a rarer medium to a denser medium, we will analyze the changes in speed and wavelength of the light ray during refraction.

### Step-by-Step Solution:

1. **Understanding the Mediums**:
- We have two mediums: a rarer medium (medium 1) and a denser medium (medium 2).
- The refractive index of the rarer medium is denoted as \( \mu_1 \) and that of the denser medium as \( \mu_2 \).

2. **Refractive Index Relationship**:
- The refractive index \( \mu \) of a medium is defined as:
\[ \mu = \frac{c}{v} \]
where \( c \) is the speed of light in vacuum and \( v \) is the speed of light in the medium.
- For the two mediums, we can write:
\[ \mu_1 = \frac{c}{v_1} \quad \text{and} \quad \mu_2 = \frac{c}{v_2} \]

3. **Comparing Refractive Indices**:
- Since medium 2 is denser than medium 1, we have \( \mu_2 > \mu_1 \).
- This implies:
\[ \frac{\mu_2}{\mu_1} > 1 \]
- From the relationship of speeds, we can write:
\[ \frac{v_1}{v_2} = \frac{\mu_2}{\mu_1} \]
- Since \( \frac{\mu_2}{\mu_1} > 1 \), it follows that:
\[ v_1 > v_2 \]
- Therefore, the speed of light decreases when it enters the denser medium.

4. **Analyzing Wavelength**:
- The wavelength \( \lambda \) of light in a medium is related to the speed of light and frequency \( f \) by the equation:
\[ \lambda = \frac{v}{f} \]
- Since the frequency of light remains constant when it passes from one medium to another, we can relate the wavelengths in the two mediums:
\[ \frac{\lambda_1}{\lambda_2} = \frac{v_1}{v_2} \]
- Since we established that \( v_1 > v_2 \), it follows that:
\[ \lambda_1 > \lambda_2 \]
- Therefore, the wavelength decreases when light enters the denser medium.

5. **Conclusion**:
- When a light ray travels from a rarer medium to a denser medium, its speed decreases and its wavelength also decreases.

### Final Answer:
- The speed of light decreases and the wavelength decreases when a light ray is refracted from a rarer medium into a denser medium.