A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

Options

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

Answer

To solve the problem, we need to find the angle of deviation (D) of a ray of light passing through an equilateral prism. Let's break down the steps:

### Step 1: Identify the Given Information
- The angle of the prism (A) = 60 degrees (since it is an equilateral prism).
- The angle of incidence (i) = angle of emergence (e) = 3/4 of the angle of the prism.

### Step 2: Calculate the Angles of Incidence and Emergence
Since the angle of the prism (A) is 60 degrees, we can calculate the angles of incidence and emergence:
- \( i = e = \frac{3}{4} \times A = \frac{3}{4} \times 60^\circ = 45^\circ \)

### Step 3: Use the Prism Formula
For a prism, the angle of deviation (D) can be calculated using the formula:
\[ D = i + e - A \]

### Step 4: Substitute the Values
Now substitute the values we found:
- \( D = 45^\circ + 45^\circ - 60^\circ \)

### Step 5: Calculate the Angle of Deviation
Now, calculate D:
- \( D = 90^\circ - 60^\circ = 30^\circ \)

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

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