An equilateral prism produces a minimum deviation of `30^(@)`. The angle of incidence is

Options

A. (a)`120^(@)`
B. (b)`60^(@)`
C. (c)`90^(@)`
D. (d)none of these

Answer

To find the angle of incidence for an equilateral prism that produces a minimum deviation of \(30^\circ\), we can follow these steps:

### Step 1: Identify the properties of the equilateral prism
An equilateral prism has all its angles equal to \(60^\circ\). Therefore, the angle of the prism \(A\) is:
\[ A = 60^\circ \]

### Step 2: Use the formula for minimum deviation
The relationship between the angle of incidence (\(i\)), angle of prism (\(A\)), and minimum deviation (\(\delta_m\)) is given by the formula:
\[ 2i = A + \delta_m \]
Where:
- \(i\) is the angle of incidence
- \(A\) is the angle of the prism
- \(\delta_m\) is the minimum deviation

### Step 3: Substitute the known values
We know that:
- \(A = 60^\circ\)
- \(\delta_m = 30^\circ\)

Substituting these values into the formula:
\[ 2i = 60^\circ + 30^\circ \]
\[ 2i = 90^\circ \]

### Step 4: Solve for the angle of incidence
Now, we divide both sides by 2 to find \(i\):
\[ i = \frac{90^\circ}{2} = 45^\circ \]

### Conclusion
The angle of incidence is \(45^\circ\).