A ray passes through a prism of angle `60^(@)` in minimum deviation position and suffers a deviation of `30^(@)`. What is the angle of incidence on the prism

Options

A. `30^@`
B. `60^@`
C. `45^@`
D. `80^@`

Answer

To find the angle of incidence on the prism when a ray passes through it in minimum deviation position, we can follow these steps:

### Step 1: Understand the Given Information
- The angle of the prism (A) is given as \(60^\circ\).
- The angle of minimum deviation (\(D_m\)) is given as \(30^\circ\).

### Step 2: Use the Formula for Minimum Deviation
In the case of minimum deviation, the relationship between the angle of incidence (\(I\)), angle of refraction (\(R\)), and the angle of the prism is given by the formula:
\[ D_m = 2I - A \]
Where:
- \(D_m\) = Minimum deviation
- \(I\) = Angle of incidence (which is equal to the angle of emergence in minimum deviation)
- \(A\) = Angle of prism

### Step 3: Substitute the Known Values
Substituting the known values into the formula:
\[ 30^\circ = 2I - 60^\circ \]

### Step 4: Rearranging the Equation
Now, rearranging the equation to solve for \(I\):
\[ 2I = 30^\circ + 60^\circ \]
\[ 2I = 90^\circ \]

### Step 5: Solve for Angle of Incidence
Dividing both sides by 2 gives:
\[ I = \frac{90^\circ}{2} = 45^\circ \]

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

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