Two plane mirrror are inclined to each other at `70^(@)`. A ray of light is incident on one mirror. They ray after two reflections will undergo a total deviation of :

Options

A. `180^(@)`
B. `220^(@)`
C. `40^(@)`
D. Cannot be found because angle of incidence is not given

Explanation

To solve the problem of calculating the total deviation of a ray of light after two reflections from two plane mirrors inclined at an angle of \(70^\circ\), we can follow these steps:

### Step 1: Understand the Geometry of Reflection
When a ray of light strikes a plane mirror, the angle of incidence (\(i\)) is equal to the angle of reflection (\(r\)). The deviation caused by a single reflection from a mirror can be expressed as:
\[ \text{Deviation} = \pi - 2i \]
where \(\pi\) is the angle in radians (180 degrees).

### Step 2: Analyze the Two Mirrors
Since there are two mirrors inclined at \(70^\circ\), we need to consider the total deviation after two reflections. The total deviation after two reflections can be expressed as:
\[ \text{Total Deviation} = \text{Deviation from Mirror 1} + \text{Deviation from Mirror 2} \]

### Step 3: Set Up the Equation
For the first mirror, the deviation is:
\[ D_1 = \pi - 2i \]
For the second mirror, the deviation is:
\[ D_2 = \pi - 2r \]
Thus, the total deviation after two reflections is:
\[ \text{Total Deviation} = (\pi - 2i) + (\pi - 2r) = 2\pi - 2(i + r) \]

### Step 4: Relate Angles
From the geometry of the situation, we know that the sum of angles around the point where the mirrors meet must equal \(180^\circ\):
\[ 90^\circ - i + 90^\circ - r + 70^\circ = 180^\circ \]
This simplifies to:
\[ 180^\circ - (i + r) + 70^\circ = 180^\circ \]
Thus:
\[ i + r = 70^\circ \]

### Step 5: Substitute and Calculate
Now we can substitute \(i + r\) back into the total deviation equation:
\[ \text{Total Deviation} = 2\pi - 2(70^\circ) \]
Converting \(70^\circ\) to radians (since \(\pi\) is in radians):
\[ 70^\circ = \frac{70 \times \pi}{180} = \frac{7\pi}{18} \]
Thus:
\[ \text{Total Deviation} = 2\pi - 2 \times \frac{7\pi}{18} \]
Calculating this gives:
\[ \text{Total Deviation} = 2\pi - \frac{14\pi}{18} = 2\pi - \frac{7\pi}{9} \]
Finding a common denominator:
\[ \text{Total Deviation} = \frac{18\pi}{9} - \frac{7\pi}{9} = \frac{11\pi}{9} \]

### Step 6: Convert Back to Degrees
To convert back to degrees:
\[ \text{Total Deviation} = \frac{11\pi}{9} \times \frac{180}{\pi} = \frac{11 \times 180}{9} = 220^\circ \]

### Conclusion
The total deviation of the ray of light after two reflections from the mirrors is \(220^\circ\).