Under minimum deviation condition in a prism, if a ray is incident at an angle `30^(@)`, the angle between the emergent ray and the second refracting surface of the prism is

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Explanation

To solve the problem, we need to find the angle between the emergent ray and the second refracting surface of the prism under the condition of minimum deviation. Here’s a step-by-step solution:

### Step 1: Understand the Geometry of the Prism
In a prism, when light enters and exits, it refracts at two surfaces. Under the condition of minimum deviation, the angle of incidence (I) is equal to the angle of emergence (E). This means that the light ray entering the prism at a certain angle will emerge at the same angle on the opposite side.

### Step 2: Identify the Given Information
From the problem, we know:
- The angle of incidence (I) = 30 degrees.

### Step 3: Use the Formula for the Angle Between the Emergent Ray and the Second Refracting Surface
The angle between the emergent ray and the second refracting surface of the prism can be calculated using the formula:
\[ \text{Angle} = 90^\circ - \text{Angle of Incidence} \]

### Step 4: Substitute the Given Angle into the Formula
Now, substituting the given angle of incidence into the formula:
\[ \text{Angle} = 90^\circ - 30^\circ \]

### Step 5: Calculate the Result
Perform the subtraction:
\[ \text{Angle} = 60^\circ \]

### Conclusion
Therefore, the angle between the emergent ray and the second refracting surface of the prism is **60 degrees**.

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