# 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.

Mentor
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?

Mentor
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..

Mentor
Consider the slope of those lines.

PhysicsMan999
They would be the same I believe.

Mentor
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

Mentor
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)

Mentor
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