Thread: mirror and beam reflection

The drawing shows a laser beam shining on a plane mirror that is perpendicular to the floor. The beam's angle of incident is = 33.7°. The beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the floor. After the reflection, how far from the base of the mirror does the beam strike the floor?

image: http://img529.imageshack.us/img529/6017/p254ps7.gif

also, for this problem I don't think were using units either?

Well, I think you have to use the Law of Sines. First we need to know at what height of the mirror the beam strikes, so using the law of sines you get

sin(56.3)/1.10 = sin(33.7)/x1
where x1 is the height at which the beam strikes.
solving for x1=(1.10)(sin(33.7))/sin(56.3)=0.73

Now we can apply the law of sines to know how far from the base of the mirror does the beam strike the floor, lets call that x2.

sin(33.7)/1.07=sin(56.3)/x2

Solving for x2,


x2=(1.07)(sin(56.3))/sin(33.7)=1.60

So the final answer is 1.60 m. All the angles are in degrees

thankyou, I knew there was trig involved it looked very familiar. Yes, solving for x2 the distance, thanks for the equation set up. Thats how I usually set up my equations, I like eliminating the variable. Thanks for the help.

I'm glad I could help you out