For any prism, prove that .n. or `mu= (sin ((A + delta_(m))/(2)))/(sin ((A)/(2)))` where the terms have their usual meaning

Explanation

To prove the relation \( n \) or \( \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \) for a prism, we will follow these steps:

### Step 1: Understand the Geometry of the Prism
Consider a prism with an apex angle \( A \). A ray of light PQ enters the prism at face AB at an angle of incidence \( I \) and is refracted at an angle \( R \). The ray then travels through the prism and exits at face AC at an angle of refraction \( R' \) and angle of emergence \( I' \).

**Hint:** Draw a diagram of the prism and label all angles and points for clarity.

### Step 2: Apply the Angle Relationships
...