UNO High School Problem of the Week Competition

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Problem 10



A photon is a particle of light that travels at a constant speed (it never stops). This speed is: meters per second (approx).


Now consider the following problem:


Two mirrors are at a distance of 2 meters apart as shown in the following picture:





These mirrors are going to move toward each other at a speed of 0.5 meters per second (each mirror has this speed). Just before they start moving, by magic a photon appears at mirror 1 and starts moving toward mirror 2. As you all know, mirrors reflect light so when the photon hits mirror 2 it will be reflected and will start traveling toward mirror 1 then again it will be reflected and will travel to mirror 2 etc.


(In reality it won’t be the same photon! The mirror absorbs the photon and a new photon is emitted.)


Assuming the photon travels perpendicularly to each mirror i.e. it won’t be reflected at some angle, how much distance (in meters) will the photon travel before the mirrors collide?



Solution