A ray of light is incident at an angle of `60^(@)` on one face of a prism of angle `30^(@)`. The ray emerging out of the prism makes an angle of `30^(@)` with the incident ray. The emergent ray is

Options

A. `0^(@)`
B. `45^(@)`
C. `90^(@)`
D. `30^(@)`

Answer

To solve the problem, we need to determine the angle of the emergent ray as it exits the prism. Here's a step-by-step solution:

### Step 1: Understand the given information
We are given:
- Angle of incidence (i) = 60°
- Angle of the prism (A) = 30°
- Angle between the incident ray and the emergent ray (Δ) = 30°

### Step 2: Use the formula for the angle of deviation
The angle of deviation (Δ) for a prism can be expressed using the formula:
\[ \Delta = i + e - A \]
where:
- \(i\) = angle of incidence
- \(e\) = angle of emergence
- \(A\) = angle of the prism

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 30° = 60° + e - 30° \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 30° = 60° + e - 30° \]
\[ 30° = 30° + e \]

### Step 5: Solve for the angle of emergence (e)
To isolate \(e\), we can subtract 30° from both sides:
\[ 30° - 30° = e \]
\[ 0° = e \]

### Conclusion
The angle of emergence \(e\) is 0°. This means that the emergent ray is parallel to the base of the prism.

### Final Answer
The emergent ray is at an angle of 0° with respect to the normal at the exit face of the prism.

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