Write a relation for the angle of deviation `(delta)` for a ray of light passing through an equilateral prism in terms of the angle of incidence `(i_(1))`, angle of emergence `(i_(2))` ang angle of prism (A).

Answer

To derive the relation for the angle of deviation (Δ) for a ray of light passing through an equilateral prism in terms of the angle of incidence (i₁), angle of emergence (i₂), and angle of the prism (A), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Angles**:
- Let i₁ be the angle of incidence at the first face of the prism.
- Let i₂ be the angle of emergence at the second face of the prism.
- Let A be the angle of the prism.

2. **Definition of Angle of Deviation**:
- The angle of deviation (Δ) is defined as the angle between the direction of the incident ray and the direction of the emergent ray.

3. **Using the Relation**:
- The relation for the angle of deviation can be expressed as:
\[ Δ = i₁ + i₂ - A \]
- This equation states that the angle of deviation is equal to the sum of the angle of incidence and the angle of emergence minus the angle of the prism.

4. **Final Relation**:
- Therefore, the final relation for the angle of deviation (Δ) in terms of the angles of incidence (i₁), emergence (i₂), and the angle of the prism (A) is:
\[ Δ = i₁ + i₂ - A \]