Light rays reflected off vertical mirror (law of reflection)

[PhysicsMan999]

Homework Statement

1. 
   A vertical mirror is placed at the origin. A ray of light coming from A is reflected by the mirror so that it passes through B. How far from the bottom does the ray hit the mirror? The coordinates are A = (11.4, 15.9) and B = (15.9, 4.7), in centimetres.
   

Homework Equations

incident angle=reflected angle
tan@=tan@=h/x

The Attempt at a Solution

So, I drew my diagram, and I know that the rule of reflection means that the incident angle from A will be equal to the reflective angle to B. I'm just trying to use trig to solve it but I'm having no luck. I drew a triangle connecting A an B, with it having a hypotenuse of 12.07, solved for its other angles, and cannot seem to relate it to the mirror height.

 

[Doc Al]

Here's a hint. Call point C where the light ray hits the mirror. Imagine lines (rays) from A to C and from C to B. How are those lines related?

 

[PhysicsMan999]

They're both arriving at/leaving C at the same angle right?

 

[Doc Al]

They're both arriving at/leaving C at the same angle right?

Good. What other property of a line expresses the angle it makes?

 

[PhysicsMan999]

Can you elaborate on that a bit? I'm not really sure what you mean..

 

[Doc Al]

Consider the slope of those lines.

 

[PhysicsMan999]

They would be the same I believe.

 

[Doc Al]

They would be the same I believe.

Draw yourself a picture and see. How is slope defined?

 

[PhysicsMan999]

rise/run. the C-B slope would just be the negative of A-B's slope. I've had the picture for awhile I just can't figure out how to get the right info to solve it

 

[Doc Al]

rise/run. the C-B slope would just be the negative of A-B's slope.

Exactly! You'll need to express that mathematically.

I've had the picture for awhile I just can't figure out how to get the right info to solve it

You are given the coordinates of A and B. Set up an equation, and you can solve for the unknown height of C.

 

[PhysicsMan999]

so the equation i set up was:
15.9-c/11.4= -((c-4.7)/15.9)
This is giving me an answer that makes no sense (68.08cm)

 

[Doc Al]

so the equation i set up was:
15.9-c/11.4= -((c-4.7)/15.9)

Almost. You messed up the sign.

 

[PhysicsMan999]

Ahhh, I see now. Thank you very much! I was trying to solve it a completely different way haha no wonder I couldn't figure it out