In an equilateral triangular prism , the angle of minimum deviation for monochromatic ray of light is `38^(@)` . What is corresponding angle of incidence ?

Options

A. `35^(@)`
B. `40^(@)`
C. `49^(@)`
D. `52^(@)`

Explanation

To find the corresponding angle of incidence for a monochromatic ray of light passing through an equilateral triangular prism with a minimum deviation of \(38^\circ\), we can follow these steps:

### Step 1: Understand the relationship in a prism
In any prism, the relationship between the angle of incidence (I), angle of emergence (E), angle of the prism (A), and the angle of minimum deviation (\(D\)) is given by the formula:
\[ I + E = A + D \]

### Step 2: Special condition at minimum deviation
At the angle of minimum deviation, the angle of incidence is equal to the angle of emergence (I = E). Therefore, we can rewrite the equation as:
\[ I + I = A + D \]
or
\[ 2I = A + D \]

### Step 3: Substitute the known values
In this case, we know:
- The angle of the prism \(A\) for an equilateral triangle is \(60^\circ\).
- The angle of minimum deviation \(D\) is given as \(38^\circ\).

Now, substituting these values into the equation:
\[ 2I = 60^\circ + 38^\circ \]

### Step 4: Calculate the angle of incidence
Now, calculate the right-hand side:
\[ 2I = 98^\circ \]
To find \(I\), divide both sides by 2:
\[ I = \frac{98^\circ}{2} = 49^\circ \]

### Conclusion
The corresponding angle of incidence is \(49^\circ\).

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