Two plane mirrors are inclined at `70^@`. A ray incident on one mirror at incidence angle `theta` after reflection falls on the second mirror and is reflected from there parallel to the first mirror, The value of `theta` is

Options

A. `50^(@)`
B. `45^(@)`
C. `30^(@)`
D. `25^(@)`

Explanation

To solve the problem of finding the angle of incidence \( \theta \) when a ray of light reflects off two inclined plane mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**: We have two plane mirrors inclined at an angle of \( 70^\circ \). A ray of light strikes the first mirror at an angle \( \theta \) and is reflected towards the second mirror, where it is reflected parallel to the first mirror.

2. **Draw the Diagram**:
- Let the first mirror be horizontal and the second mirror inclined at \( 70^\circ \) to the first.
- The incident ray strikes the first mirror at angle \( \theta \) with respect to the normal (perpendicular) to the mirror.

3. **Identify Angles**:
- The angle of incidence \( \theta \) is equal to the angle of reflection from the first mirror.
- Let’s denote the angle between the normal to the first mirror and the incident ray as \( \theta \).
- After reflecting off the first mirror, the ray will strike the second mirror.

4. **Calculate the Angle of Reflection**:
- According to the law of reflection, the angle of incidence equals the angle of reflection. Therefore, the angle of reflection from the first mirror is also \( \theta \).

5. **Determine the Angle with the Second Mirror**:
- The angle between the first mirror and the second mirror is \( 70^\circ \).
- The angle between the reflected ray and the normal to the second mirror can be calculated as:
\[ 90^\circ - (70^\circ - \theta) = 90^\circ - 70^\circ + \theta = 20^\circ + \theta \]

6. **Set Up the Parallel Condition**:
- After reflecting off the second mirror, the ray is parallel to the first mirror. This means the angle of reflection from the second mirror must also be \( 0^\circ \) with respect to the first mirror.
- Therefore, the angle of incidence on the second mirror must equal \( 20^\circ + \theta \).

7. **Using the Reflection Law on the Second Mirror**:
- The angle of incidence on the second mirror also equals the angle of reflection. Since the ray is reflected parallel to the first mirror, we can set:
\[ 20^\circ + \theta = 70^\circ \]

8. **Solve for \( \theta \)**:
\[ \theta = 70^\circ - 20^\circ = 50^\circ \]

### Final Answer:
The value of \( \theta \) is \( 50^\circ \).

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