If a plane mirror is rotated in its ownplane through an angle of 20° keeping the incident ray direction fixed, then the angle through which the reflected ray turns is

Options

A. `40^@`
B. `0^@`
C. `20^@`
D. `10^@`

Explanation

To solve the problem of how much the reflected ray turns when a plane mirror is rotated through an angle of 20° while keeping the incident ray direction fixed, we can follow these steps:

### Step 1: Understand the Reflection Law
The law of reflection states that the angle of incidence (i) is equal to the angle of reflection (r). This means that if the mirror is rotated, both the angle of incidence and the angle of reflection will change.

### Step 2: Analyze the Rotation of the Mirror
When the mirror is rotated by an angle θ (in this case, 20°), the angle of reflection will also change. The total change in the angle of reflection will be twice the angle of rotation of the mirror.

### Step 3: Calculate the Change in the Reflected Ray
If the mirror is rotated by 20°, the angle of reflection will change by:
\[ \text{Change in reflected angle} = 2 \times \text{Angle of rotation} = 2 \times 20° = 40° \]

### Step 4: Conclusion
Thus, when the plane mirror is rotated through an angle of 20°, the reflected ray will turn through an angle of 40°.

### Final Answer
The angle through which the reflected ray turns is **40°**.

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