A ray of light is incident at `50^(@)` on the middle of one of two mirrors arranged at an angle of `60^(@)` between them. They ray then touches the second mirror, get reflected back to the first mirror, making an anlge of incidence of

Options

A. `50^(@)`
B. `60^(@)`
C. `70^(@)`
D. `80^(@)`

Answer

To solve the problem step by step, we will analyze the situation involving the two mirrors and the ray of light.

### Step 1: Understand the Geometry
We have two mirrors arranged at an angle of \(60^\circ\) between them. A ray of light is incident on the first mirror at an angle of \(50^\circ\).

### Step 2: Identify the Angle of Reflection
According to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, when the ray hits the first mirror, it reflects off at the same angle of \(50^\circ\).

### Step 3: Calculate the Angle with Respect to the Normal
The angle between the normal to the mirror and the ray is \(50^\circ\). The angle between the two mirrors is \(60^\circ\), so we can find the angle between the reflected ray and the second mirror.

- The angle between the normal to the first mirror and the line connecting the two mirrors is \(90^\circ - 50^\circ = 40^\circ\).
- Thus, the angle between the reflected ray and the second mirror is:
\[ 60^\circ - 40^\circ = 20^\circ \]

### Step 4: Determine the Angle of Incidence on the Second Mirror
The angle of incidence on the second mirror is equal to the angle of reflection from the first mirror, which is \(20^\circ\).

### Step 5: Reflecting Back to the First Mirror
When the ray reflects off the second mirror, it will again follow the law of reflection. The angle of incidence on the second mirror is \(20^\circ\), so the angle of reflection will also be \(20^\circ\).

### Step 6: Calculate the Angle of Incidence on the First Mirror for the Second Time
Now, we need to find the angle of incidence on the first mirror when the ray returns.

1. The total angle around the normal at the first mirror is \(90^\circ\).
2. Since the angle of reflection from the second mirror is \(20^\circ\), the angle with respect to the normal at the first mirror is:
\[ 90^\circ - 20^\circ = 70^\circ \]

Thus, the angle of incidence on the first mirror for the second time is \(70^\circ\).

### Conclusion
The angle of incidence on the first mirror for the second time is \(70^\circ\).

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