Which of the following graphs is the correct angle of incidence vs. angle of deviation graph?

Options

A.
B.
C.
D.

Answer

To determine the correct angle of incidence vs. angle of deviation graph for a prism, we can follow these steps:

### Step 1: Understand the Concept of Deviation
The angle of deviation (δ) is the angle between the direction of the incident ray and the direction of the emergent ray after passing through the prism. The deviation depends on the angle of incidence (I) and the prism's apex angle (A).

**Hint:** Remember that deviation is influenced by how light bends when it enters and exits the prism.

### Step 2: Analyze the Relationship Between Incidence and Deviation
As the angle of incidence increases, the angle of deviation initially decreases until it reaches a minimum point. After this minimum point, as the angle of incidence continues to increase, the angle of deviation starts to increase again. This creates a characteristic curve.

**Hint:** Consider how light behaves at different angles of incidence. Think about the bending of light at the boundaries of the prism.

### Step 3: Identify Key Points on the Graph
1. **Minimum Deviation Point:** There exists a specific angle of incidence (I) where the deviation is at its minimum. This occurs when the light passes symmetrically through the prism.
2. **Symmetry:** For two different angles of incidence (I1 and I2), the deviation can be the same. This means the graph will show that two different angles can yield the same deviation.

**Hint:** Look for points on the graph where the deviation is the same for two different angles of incidence.

### Step 4: Determine the Shape of the Graph
The graph of angle of incidence (I) vs. angle of deviation (δ) typically shows a U-shape or a parabolic curve. It starts high, decreases to a minimum, and then increases again.

**Hint:** Visualize the behavior of the light as it enters and exits the prism. The graph should reflect this behavior.

### Step 5: Choose the Correct Graph
Based on the analysis, the correct graph will show:
- A minimum point of deviation.
- Symmetrical behavior for two angles of incidence leading to the same deviation.
- An overall U-shape or parabolic curve.

**Hint:** Compare the options provided with the characteristics discussed to identify the correct graph.

### Conclusion
The correct angle of incidence vs. angle of deviation graph will exhibit a U-shaped curve with a minimum deviation point, indicating the relationship between the angle of incidence and the resulting angle of deviation through the prism.

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