Two vertical plane mirrors are inclined at an angle of `60^(@)` with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

Options

A. `60^(@)`
B. `120^(@)`
C. `180^(@)`
D. `240^(@)`

Answer

To solve the problem of finding the resultant deviation of a ray of light reflected between two vertical mirrors inclined at an angle of \(60^\circ\), we can follow these steps:

### Step 1: Understand the Geometry of the Setup
We have two vertical mirrors inclined at an angle of \(60^\circ\). When a ray of light travels horizontally and strikes the first mirror, it will reflect off that mirror and then strike the second mirror.

### Step 2: Analyze the First Reflection
When the ray strikes the first mirror, it will reflect according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection. Since the ray is traveling horizontally, the angle of incidence with respect to the normal (which is vertical) will be \(0^\circ\). Therefore, the angle of reflection will also be \(0^\circ\), and the ray will continue horizontally towards the second mirror.

### Step 3: Analyze the Second Reflection
Now, when the ray reaches the second mirror, it will strike it at an angle. The angle between the incoming ray and the normal to the second mirror will be \(60^\circ\) (the angle between the two mirrors). Thus, the angle of incidence at the second mirror is \(60^\circ\), and by the law of reflection, the angle of reflection will also be \(60^\circ\).

### Step 4: Calculate the Total Deviation
The total deviation caused by the two reflections can be calculated as follows:
1. The first reflection does not change the direction of the ray (deviation = \(0^\circ\)).
2. The second reflection changes the direction of the ray by \(60^\circ\) (deviation = \(60^\circ\)).
3. However, since the ray is reflected off the second mirror, we need to consider the total deviation from the original direction. The total deviation is given by:
\[ \text{Total Deviation} = 180^\circ - \text{Angle between mirrors} \]
Therefore, the total deviation is:
\[ \text{Total Deviation} = 180^\circ - 60^\circ = 120^\circ \]

### Step 5: Final Result
Thus, the resultant deviation of the ray after reflecting off both mirrors is \(120^\circ\).

### Summary
The total deviation of the ray of light after reflecting off both mirrors is \(120^\circ\).

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