Two plane mirrors are inclined to each other at some angle. A ray of light is incident on one of them at an angle of `35^@`. The light after reflection falls on the second mirror and gets reversed. The angle between the mirrors is

Options

A. `17.5^@`
B. `35^@`
C. `52.2^@`
D. `70^@`

Answer

To solve the problem of finding the angle between two plane mirrors when a ray of light is incident on one of them at an angle of \(35^\circ\) and gets reversed after reflection from the second mirror, 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 an angle of incidence \(i = 35^\circ\).

2. **Applying the Law of Reflection**:
According to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, the angle of reflection \(r_1\) from the first mirror is also \(35^\circ\).

3. **Analyzing the Reflection**:
The ray after reflecting from the first mirror will strike the second mirror. The angle between the reflected ray and the normal to the second mirror will be \((\theta + 35^\circ)\) since the angle between the two mirrors is \(\theta\).

4. **Using the Law of Reflection Again**:
When the ray hits the second mirror, it will reflect off at the same angle it strikes. Therefore, the angle of incidence on the second mirror will be \((\theta + 35^\circ)\) and the angle of reflection \(r_2\) will also be \((\theta + 35^\circ)\).

5. **Setting Up the Equation**:
For the ray to be reversed after reflection from the second mirror, the total angle of incidence and reflection must equal \(180^\circ\). Thus, we can set up the equation:
\[ r_1 + r_2 = 180^\circ \]
Substituting the values we have:
\[ 35^\circ + (\theta + 35^\circ) = 180^\circ \]

6. **Solving for \(\theta\)**:
Simplifying the equation:
\[ 35^\circ + \theta + 35^\circ = 180^\circ \]
\[ \theta + 70^\circ = 180^\circ \]
\[ \theta = 180^\circ - 70^\circ \]
\[ \theta = 110^\circ \]

7. **Conclusion**:
The angle between the two mirrors is \(\theta = 110^\circ\).