Rays of light pass through an equilateral prism such that the angle of incidence is equal to the angle of emergence and the latter is equal three-fourths the angle of the prism. The angle of deviation is

Options

A. `45 ^(@)`
B. `39^(@)`
C. `20^(@)`
D. `30^(@)`

Answer

To solve the problem step by step, we need to determine the angle of deviation when light passes through an equilateral prism with given conditions.

### Step 1: Understand the given information
- The prism is equilateral, which means the angle of the prism (A) is 60 degrees.
- The angle of incidence (i) is equal to the angle of emergence (e).
- The angle of incidence and emergence is equal to three-fourths of the angle of the prism.

### Step 2: Calculate the angle of incidence and emergence
Since the angle of incidence and emergence (i = e) is three-fourths of the angle of the prism:
\[ i = e = \frac{3}{4} \times A \]
Substituting the value of A (60 degrees):
\[ i = e = \frac{3}{4} \times 60 = 45 \text{ degrees} \]

### Step 3: Use the formula for angle of deviation
The angle of deviation (Δ) can be calculated using the formula:
\[ Δ = i + e - A \]
Substituting the values we have:
\[ Δ = 45 + 45 - 60 \]

### Step 4: Calculate the angle of deviation
Now, simplifying the equation:
\[ Δ = 90 - 60 = 30 \text{ degrees} \]

### Step 5: Conclusion
The angle of deviation when light passes through the prism is 30 degrees.

### Final Answer
The angle of deviation is **30 degrees**.

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