When a ray of light is incident normally on one refracting surface of an equilateral prism (Refractive index of the material of the prism `=1.5`

Options

A. emerging ray is deviated by `30^(@)`
B. emerging ray is deviated by `45^(@)`
C. emerging ray just grazes the second refracting surface
D. the ray undergoes total internal reflection at the second refracting surface

Explanation

To solve the problem step by step, we will analyze the situation of a ray of light incident normally on one refracting surface of an equilateral prism with a refractive index of 1.5.

### Step-by-Step Solution:

1. **Understanding the Prism Geometry**:
- An equilateral prism has angles of 60 degrees each. When a ray of light is incident normally on one of its surfaces, it means that the angle of incidence (i) at that surface is 0 degrees. However, we need to consider the path of the ray as it enters the prism and interacts with the second surface.

2. **Finding the Angle of Refraction**:
- Since the ray is incident normally, it will pass straight through the first surface without bending. Thus, the angle of refraction (r1) at the first surface is also 0 degrees.

3. **Determining the Angle of Incidence at the Second Surface**:
- As the ray travels through the prism, it will reach the second surface. The angle of incidence at the second surface can be calculated based on the geometry of the prism. Since the internal angle of the prism is 60 degrees, the angle of incidence (i2) at the second surface will be:
\[ i2 = 60^\circ - r1 = 60^\circ - 0^\circ = 60^\circ \]

4. **Calculating the Critical Angle**:
- To determine whether the ray will undergo total internal reflection or emerge from the prism, we need to calculate the critical angle (C) for the material of the prism using the formula:
\[ \sin C = \frac{1}{\mu} \]
- Given that the refractive index (µ) of the prism is 1.5, we have:
\[ \sin C = \frac{1}{1.5} = \frac{2}{3} \]
- Therefore, the critical angle (C) can be calculated as:
\[ C = \sin^{-1}\left(\frac{2}{3}\right) \approx 41.8^\circ \]

5. **Comparing the Angle of Incidence with the Critical Angle**:
- The angle of incidence at the second surface is 60 degrees, which is greater than the critical angle of approximately 41.8 degrees. This indicates that total internal reflection will occur.

6. **Conclusion**:
- Since the angle of incidence is greater than the critical angle, the ray will not emerge from the prism but will instead undergo total internal reflection at the second surface.

### Final Answer:
The ray undergoes total internal reflection at the second reflecting surface.