Angle of minimum deviation is equal to the angle prism A of an equilateral glass prism. The angle incidence at which minimum deviation will be obtained is

Options

A. `60^(@)`
B. `30^(@)`
C. `45^(@)`
D. `sin^(1)(2//3)`

Answer

To solve the problem, we need to find the angle of incidence at which minimum deviation occurs for an equilateral glass prism. Here are the steps to arrive at the solution:

### Step 1: Understand the condition for minimum deviation
In the case of a prism, the angle of minimum deviation (D) occurs when the angle of incidence (i) is equal to the angle of emergence (e). This means that:

\[ i = e \]

### Step 2: Apply the formula for deviation
The deviation (D) in a prism is given by the formula:

\[ D = i + e - A \]

Where:
- \( D \) is the angle of deviation,
- \( i \) is the angle of incidence,
- \( e \) is the angle of emergence,
- \( A \) is the angle of the prism.

### Step 3: Substitute the condition for minimum deviation
Since at minimum deviation \( i = e \), we can rewrite the deviation formula as:

\[ D = i + i - A \]
\[ D = 2i - A \]

### Step 4: Set the angle of minimum deviation equal to the angle of the prism
According to the problem, the angle of minimum deviation (D) is equal to the angle of the prism (A). For an equilateral prism, the angle \( A \) is 60 degrees. Thus, we have:

\[ D = A = 60^\circ \]

### Step 5: Substitute into the deviation formula
Now we can substitute \( D \) into the equation:

\[ 60^\circ = 2i - 60^\circ \]

### Step 6: Solve for the angle of incidence (i)
Rearranging the equation gives:

\[ 2i = 60^\circ + 60^\circ \]
\[ 2i = 120^\circ \]
\[ i = \frac{120^\circ}{2} \]
\[ i = 60^\circ \]

### Conclusion
The angle of incidence at which minimum deviation will be obtained is:

\[ \boxed{60^\circ} \]