What should be the angle of incidence for a ray of light which suffers minimum deviation of `36^(@)` through an equilateral prism ?

Answer

To find the angle of incidence for a ray of light that suffers minimum deviation of 36 degrees through an equilateral prism, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angle of the Prism**:
- For an equilateral prism, each angle is 60 degrees.
- Therefore, the angle of the prism \( A = 60^\circ \).

2. **Understand the Condition for Minimum Deviation**:
- At minimum deviation, the angle of incidence \( i \) is equal to the angle of emergence \( e \).
- Thus, we can express the relationship as \( i = e \).

3. **Use the Formula for Minimum Deviation**:
- The formula for the deviation \( D \) in terms of the angle of incidence \( i \) and the angle of the prism \( A \) is:
\[ D = i + e - A \]
- Since \( i = e \) at minimum deviation, we can rewrite the formula as:
\[ D = 2i - A \]

4. **Substitute the Known Values**:
- We know the minimum deviation \( D = 36^\circ \) and the angle of the prism \( A = 60^\circ \).
- Substitute these values into the equation:
\[ 36^\circ = 2i - 60^\circ \]

5. **Solve for the Angle of Incidence**:
- Rearranging the equation gives:
\[ 2i = 36^\circ + 60^\circ \]
\[ 2i = 96^\circ \]
\[ i = \frac{96^\circ}{2} = 48^\circ \]

6. **Conclusion**:
- The angle of incidence \( i \) for the ray of light is \( 48^\circ \).

### Final Answer:
The angle of incidence for a ray of light which suffers minimum deviation of \( 36^\circ \) through an equilateral prism is \( 48^\circ \).

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