A pair of vertical plane mirrors stands with an angle of β = 56.5 degrees between them. A pencil of light approaches in a direction parallel to one of them, as shown. After the pencil has left the mirrors, in which direction will it be going? (Give your answer as the angle above the second mirror the light hits... NOT as an angle with respect to the normal) Use "deg" as the unit for degrees.
http://www.physicsforums.com/showthread.php?t=200266
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To determine the direction in which the light will be going after leaving the mirrors, we need to consider the reflection properties of mirrors.
When a light ray hits a mirror, it reflects off the mirror surface according to the law of reflection. The law of reflection states that the incident angle (the angle between the incident ray and the normal to the mirror surface) is equal to the angle of reflection (the angle between the reflected ray and the normal to the mirror surface).
In this case, since the angle between the two mirrors is given as β = 56.5 degrees, the angle of reflection with respect to the normal on the first mirror will also be β = 56.5 degrees. Let's call this angle of reflection α.
Now, since the incident ray is parallel to the first mirror, the angle between the incident ray and the first mirror is 0 degrees.
Using the law of reflection, we can determine the angle between the reflected ray and the second mirror. Since the angle of reflection α is equal to the angle of incidence on the second mirror, the angle between the reflected ray and the second mirror will also be β = 56.5 degrees.
Therefore, the light will be going in the same direction as the second mirror, making an angle of β = 56.5 degrees above the second mirror.
So, the answer is 56.5 deg.