In total internal reflection when the angle of incidence is equal to the critical angle for the pair of medium in contact, what will be angle of refraction? In total internal reflection when the angle of incidence is equal to the critical angle for the pair of medium in contact, what will be angle of refraction? In total internal reflection when the angle of incidence is equal to the critical angle for the pair of medium in contact, what will be angle of refraction?

Options

A. `90^(@)`
B. `180^(@)`
C. `0^(@)`
D. equal to angle of incidence

Explanation

To solve the question regarding total internal reflection and the angle of refraction when the angle of incidence is equal to the critical angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Total Internal Reflection**:
Total internal reflection occurs when a light ray travels from a denser medium to a rarer medium and the angle of incidence exceeds the critical angle. At the critical angle, the light ray refracts along the boundary.

2. **Defining the Critical Angle**:
The critical angle (θc) is defined as the angle of incidence in the denser medium at which the angle of refraction in the rarer medium is 90 degrees. This means that the refracted ray travels along the boundary between the two media.

3. **Applying Snell's Law**:
According to Snell's Law:
\[ n_1 \sin(\theta_i) = n_2 \sin(\theta_r) \]
where:
- \( n_1 \) is the refractive index of the denser medium,
- \( n_2 \) is the refractive index of the rarer medium,
- \( \theta_i \) is the angle of incidence,
- \( \theta_r \) is the angle of refraction.

4. **Setting Up the Equation at Critical Angle**:
When the angle of incidence is equal to the critical angle (θc), we have:
\[ \theta_i = \theta_c \]
and at this point, the angle of refraction (θr) is 90 degrees. Therefore, we can substitute into Snell's Law:
\[ n_1 \sin(\theta_c) = n_2 \sin(90^\circ) \]
Since \(\sin(90^\circ) = 1\), the equation simplifies to:
\[ n_1 \sin(\theta_c) = n_2 \]

5. **Conclusion**:
At the critical angle, the angle of refraction is 90 degrees. Thus, when the angle of incidence is equal to the critical angle, the angle of refraction will be:
\[ \theta_r = 90^\circ \]

### Final Answer:
The angle of refraction when the angle of incidence is equal to the critical angle is **90 degrees**.

---