Mirror Reflection Help!

I have no idea how to solve a problem like this, and my homework has several of them. Please help me figure this out!

Problem: At what angle theta should the laser beam in the figure be aimed at the mirrored ceiling in order to hit the midpoint of the far wall?

Figure: http://session.masteringphysics.com/prob…

Thank you!

This is an interesting question; I am sorry I cannot draw you a diagram, but I will do my best to explain it.

Draw the light path from the lower left corner to the mirror. Then draw the reflected ray to the midpoint of the far wall.

Now, divide the length of the mirror into two pieces: call x the distance from the right edge of the mirror to where the light ray hits the mirror; then 5-x is the length of the rest of the mirror.

Next, use the law of reflection to show that the reflected ray makes an angle of theta with the mirror.

From this, you can show that

tan theta = 3/(5-x) and also tan(theta)=1.5/x

(construct right angles using the incident and reflected rays to do this)

now, since both expressions equal tan(theta), set them equal to each other:

3/(5-x) = 1.5/x

cross multiply and solve for x (I get theta = 41.98 deg)

once you have your value of x, find your value of theta from tan (theta)=1.5/x

Sorry, your link goes nowhere...