A ray of light passes through an equilateral prism (refractive index `1.5`) such that angle of incidence is equal to angle of emergence and the latter is equal to `3//4 th` of the angle of prism. Calculate the angle of deviation.

Options

A. `60^(@)`
B. `30^(@)`
C. `45^(@)`
D. `120^(@)`

Explanation

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Understand the Given Information
- We have an equilateral prism, which means the angle of the prism \( A = 60^\circ \).
- The refractive index \( n = 1.5 \).
- The angle of incidence \( i \) is equal to the angle of emergence \( e \).
- The angle of emergence \( e \) is given as \( \frac{3}{4} \) of the angle of the prism \( A \).

### Step 2: Express the Angles
From the information provided:
- Since the angle of emergence \( e = \frac{3}{4} A \), we can calculate \( e \):
\[ e = \frac{3}{4} \times 60^\circ = 45^\circ \]
- Since \( i = e \), we also have:
\[ i = 45^\circ \]

### Step 3: Use the Formula for Angle of Deviation
The formula for the angle of deviation \( \delta \) is given by:
\[ \delta = i + e - A \]
Substituting the values we have:
\[ \delta = 45^\circ + 45^\circ - 60^\circ \]

### Step 4: Calculate the Angle of Deviation
Now, we can perform the calculation:
\[ \delta = 90^\circ - 60^\circ = 30^\circ \]

### Step 5: Conclusion
Thus, the angle of deviation \( \delta \) is:
\[ \delta = 30^\circ \]

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

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