How to Calculate the Initial Angle of Incidence in a Mirrored Maze?

AI Thread Summary
To calculate the initial angle of incidence on mirror 1 in a mirrored maze, the law of reflection is applied, stating that the angle of incidence equals the angle of reflection. Given that the reflected angle from mirror 3 is 52° and the angle β is 12°, the initial angle of incidence on mirror 1 is determined to be 40°. The solution was reached without the need for trigonometric functions, confirming the approach's validity. The discussion seeks confirmation of this calculated angle.
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Homework Statement



In an amusement park maze with all the walls covered with mirrors, Pilar sees Hernando's reflection from a series of three mirrors. If the reflected angle from mirror 3 is 52° for the mirror arrangement shown in the figure, in which = 12°, what is the angle of incidence on mirror 1?

p23-42alt.gif


Homework Equations


law of reflection:
angle incident = angle reflected (with respect to normal)

The Attempt at a Solution



Working backwards, I arrived at 40 degrees.
 
Last edited:
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Angle \beta = 12°?
 
Yes, alpha = 52, beta = 12.

Just hope if anyone can confirm my answer. I worked it through and did not have to use trig.
 

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