You are given four sources of light each one providing a light of a single colour-red, blue,green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is `90^@`. Which of the folowing statements is correct it the source of yellow light is replaced with that of other lights without changing the angle of incidence ?

Options

A. The beam of red light would undergo total internal reflection
B. The beam of red light would bend towards normal while it gets refracted through the second mediurn
C. The beam of blue light would undergo total internal reflection
D. The beam of green light would bend away from the normal as it gets refracted through the second medium

Explanation

To solve the problem, we need to analyze the situation involving the refraction of light through different media and the concept of critical angle and total internal reflection.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have four light sources: red, blue, green, and yellow.
- The angle of refraction for yellow light at a certain angle of incidence is given as \(90^\circ\).

2. **Identifying the Critical Angle**:
- When the angle of refraction is \(90^\circ\), it indicates that the angle of incidence corresponds to the critical angle (\(\theta_c\)) for yellow light.
- According to Snell's Law:
\[ n_1 \sin(\theta_i) = n_2 \sin(\theta_r) \]
where \(\theta_i\) is the angle of incidence, \(\theta_r\) is the angle of refraction, \(n_1\) is the refractive index of the first medium, and \(n_2\) is the refractive index of the second medium.

3. **Calculating the Critical Angle**:
- Since \(\theta_r = 90^\circ\), we can rewrite Snell's Law as:
\[ n_1 \sin(\theta_i) = n_2 \cdot 1 \]
- This simplifies to:
\[ \sin(\theta_i) = \frac{n_2}{n_1} \]
- The critical angle is given by:
\[ \theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right) \]
- In this case, yellow light has a critical angle, and we can denote the refractive index of yellow light as \(n_y\).

4. **Comparing Refractive Indices**:
- The order of refractive indices for the colors is typically:
- Red (lowest), Yellow, Green, Blue (highest).
- This means \(n_r < n_y < n_g < n_b\).

5. **Replacing Yellow Light with Other Colors**:
- If we replace yellow light with red, blue, or green light while keeping the angle of incidence the same, we need to analyze what happens:
- **Red Light**: Since red has the lowest refractive index, it will have a higher critical angle than yellow. Thus, it will not undergo total internal reflection.
- **Green Light**: Green has a higher refractive index than yellow, so it will also not undergo total internal reflection.
- **Blue Light**: Blue has the highest refractive index. Therefore, it will have the lowest critical angle and will undergo total internal reflection if the angle of incidence is greater than its critical angle.

6. **Conclusion**:
- The correct statement is that if the source of yellow light is replaced with blue light, the blue light will undergo total internal reflection at the same angle of incidence.

### Final Answer:
The correct statement is that **the beam of blue light will undergo total internal reflection** when the source of yellow light is replaced with blue light.