Four similar prisms of same material having same angle of prism are arranged. Which among the four of the arrangements shown in the following figures gives no not angular deviation ?

Options

A.
B.
C.
D.

Answer

To solve the question regarding the arrangement of four similar prisms of the same material and the same angle of prism, we will analyze each arrangement to determine which one results in no angular deviation of the light ray passing through them.

### Step-by-Step Solution:

1. **Understanding the Concept of Angular Deviation**:
- When light passes through a prism, it bends towards the base of the prism. The amount of bending is quantified as angular deviation. If multiple prisms are arranged in such a way that their effects on the light ray cancel each other out, then the net angular deviation can be zero.

2. **Analyzing Arrangement A**:
- In the first arrangement, a light ray enters the first prism, bends towards the base, exits, and then enters the second prism. Each prism causes a deviation in the light ray. As the light continues through the prisms, it will have a net angular deviation.
- **Conclusion**: Arrangement A has a net angular deviation.

3. **Analyzing Arrangement B**:
- In the second arrangement, the prisms are arranged in such a way that the light ray enters the first prism, bends towards the base, and then enters the second prism. The second prism will counteract the deviation caused by the first prism, and this pattern continues with the subsequent prisms.
- Since each prism's deviation is countered by the next, the light ray will exit parallel to its original path, resulting in no net angular deviation.
- **Conclusion**: Arrangement B has no angular deviation.

4. **Analyzing Arrangement C**:
- In this arrangement, all prisms are stacked together. The light ray will pass through all prisms as if it were passing through a single prism. Since a single prism always causes some angular deviation, this arrangement will also have a net angular deviation.
- **Conclusion**: Arrangement C has a net angular deviation.

5. **Analyzing Arrangement D**:
- In the fourth arrangement, the prisms are arranged in a way that resembles a single prism with a 90-degree angle. The light ray will bend towards the base and then exit, resulting in a net angular deviation.
- **Conclusion**: Arrangement D has a net angular deviation.

### Final Answer:
The arrangement that gives no angular deviation is **Arrangement B**.