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Shown in the figure are two plane mirrors XY and Y'Z (XY L YZ) joined at their edge. Also shown is a light ray falling on one of the irrors and reflected back parallel to its original path as a result of this arrangement. The two mirrors are now rotated by an angle θ to their new position XYZ', as shown. As a result the new reflected ray is at an angle a from the original reflected ray. Then :
a = 0
α = θ
α = 2θ
α = 4θ
- Option 1: a = 0
The angle a is not zero, as rotating the mirrors will change the direction of the reflected ray.
- Option 2: a = ?
This suggests that the change in angle of the reflected ray is equal to the rotation angle of the mirrors.
- Option 3: a = 2?
Each mirror contributes half of the total change in the angle of the reflected ray, making the angle change equal to twice the rotation angle.
- Option 4: a = 4?
This option accounts for both mirrors contributing twice, which is accurate for this configuration.
Correct Answer: Option 4: a = 4?
When the mirrors are rotated by an angle ?, the geometry results in a total rotation of the angles for the reflected ray equaling 4?.
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