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. (a) `45^(@)`
B. (b) `39^(@)`
C. (c) `20^(@)`
D. (d) `30^(@)`

Explanation

To solve the problem step by step, we will follow the information provided in the question and apply the relevant concepts of optics.

### Step 1: Understand the given information
We have an equilateral glass prism, which means that the angle of the prism (A) is 60 degrees. We are given that the angle of incidence (I) is equal to the angle of emergence (E) and both are equal to 3/4 of the angle of the prism.

### Step 2: Calculate the angle 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: Identify the condition of minimum deviation
When the angle of incidence is equal to the angle of emergence, it indicates that the ray of light is experiencing the minimum deviation. In this case, we denote the minimum angle of deviation as \( D_m \).

### Step 4: Use the formula for minimum deviation
The formula for the minimum angle of deviation in terms of the angle of incidence and the angle of the prism is given by:
\[ D_m = 2I - A \]
Substituting the values we have:
\[ D_m = 2 \times 45^\circ - 60^\circ \]

### Step 5: Calculate the minimum angle of deviation
Now, we can perform the calculation:
\[ D_m = 90^\circ - 60^\circ = 30^\circ \]

### Conclusion
The angle of deviation is \( 30^\circ \).

### Final Answer
The angle of deviation is \( 30^\circ \).

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