Two plane mirrors are inclined to each other at an angle `theta`. A ray of light is reflected at one
mirror and then at the other. Find the total deviation of the ray.

Explanation

To solve the problem of finding the total deviation of a ray of light reflected between two inclined plane mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors inclined at an angle \( \theta \).
- A ray of light strikes the first mirror at point A, reflects, and then strikes the second mirror at point B.

2. **Drawing the Diagram**:
- Draw two inclined mirrors intersecting at point O, making an angle \( \theta \).
- Draw the incident ray hitting mirror 1 at point A and the normal line to mirror 1 at point A.

3. **Applying the Law of Reflection at Mirror 1**:
- Let the angle of incidence at mirror 1 be \( I \).
- According to the law of reflection, the angle of reflection will also be \( I \).

4. **Finding the Angle of Incidence at Mirror 2**:
- The angle between the normal to mirror 1 and the normal to mirror 2 is \( 90^\circ - I + \theta \).
- Therefore, the angle of incidence at mirror 2 can be found as:
\[ \text{Angle of incidence at mirror 2} = \theta - I \]

5. **Calculating the Angle of Deviation at Each Mirror**:
- **For Mirror 1**:
- The angle of deviation \( \delta_1 \) is given by:
\[ \delta_1 = 180^\circ - 2I \]
- **For Mirror 2**:
- The angle of deviation \( \delta_2 \) is given by:
\[ \delta_2 = 180^\circ - 2(\theta - I) = 180^\circ - 2\theta + 2I \]

6. **Finding the Total Angle of Deviation**:
- The total angle of deviation \( \delta_{\text{total}} \) is the sum of the deviations from both mirrors:
\[ \delta_{\text{total}} = \delta_1 + \delta_2 \]
- Substituting the values:
\[ \delta_{\text{total}} = (180^\circ - 2I) + (180^\circ - 2\theta + 2I) \]
- Simplifying this expression:
\[ \delta_{\text{total}} = 360^\circ - 2\theta \]

7. **Final Result**:
- Thus, the total deviation of the ray after reflecting off both mirrors is:
\[ \delta_{\text{total}} = 360^\circ - 2\theta \]