A prism splits up light into different colours but a glass slab does not show dispersion because

Options

A. The emergent ray is deviated from the direction of the incident ray by the angle of deviation
B. The incident and emergent rays are parallel to each other
C. The emergent ray is laterally displaced from glass slab and changes its direction
D. The incident and emergent rays are not parallel to each other.

Explanation

To solve the question, "A prism splits up light into different colours but a glass slab does not show dispersion because," we need to analyze the options provided and understand the principles of light refraction and dispersion.

### Step-by-Step Solution:

1. **Understanding Dispersion**:
- Dispersion is the phenomenon where white light is separated into its constituent colors when it passes through a medium. This occurs due to the different wavelengths of light being refracted by different amounts.

2. **Analyzing the Prism**:
- A prism has angled surfaces that are not parallel. When light enters a prism, it refracts at the first surface and again at the second surface. The different colors of light are refracted by different angles due to their varying wavelengths, resulting in a spectrum of colors.

3. **Analyzing the Glass Slab**:
- A glass slab has parallel sides. When light enters the slab, it refracts at the first surface and then refracts again at the second surface. However, since the sides are parallel, the angle of incidence and the angle of refraction at the second surface are equal and opposite, causing the emergent ray to be parallel to the incident ray.

4. **Evaluating the Options**:
- **Option A**: The emergent ray is deviated from the direction of the incident ray by the angle of deviation. (Incorrect, as the emergent ray is parallel to the incident ray in a slab.)
- **Option B**: The incident and emergent rays are parallel to each other. (Correct, this is why there is no dispersion in a glass slab.)
- **Option C**: The emergent ray is literally displaced from the glass slab and changes its direction. (Incorrect, the emergent ray does not change direction significantly.)
- **Option D**: The incident and emergent rays are not parallel to each other. (Incorrect, they are parallel in a glass slab.)

5. **Conclusion**:
- The correct answer is **Option B**: The incident and emergent rays are parallel to each other. This is why a glass slab does not show dispersion, as the parallel sides of the slab neutralize the effects of dispersion that occur at the entry and exit points.

### Final Answer:
A prism splits up light into different colours but a glass slab does not show dispersion because the incident and emergent rays are parallel to each other (Option B).