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Light rays reflected off vertical mirror (law of reflection)

  • #1

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.
 

Answers and Replies

  • #2
Doc Al
Mentor
44,892
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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?
 
  • #3
They're both arriving at/leaving C at the same angle right?
 
  • #4
Doc Al
Mentor
44,892
1,143
They're both arriving at/leaving C at the same angle right?
Good. What other property of a line expresses the angle it makes?
 
  • #5
Can you elaborate on that a bit? I'm not really sure what you mean..
 
  • #6
Doc Al
Mentor
44,892
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Consider the slope of those lines.
 
  • #7
They would be the same I believe.
 
  • #8
Doc Al
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44,892
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They would be the same I believe.
Draw yourself a picture and see. How is slope defined?
 
  • #9
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
 
  • #10
Doc Al
Mentor
44,892
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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.
 
  • #11
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)
 
  • #12
Doc Al
Mentor
44,892
1,143
so the equation i set up was:
15.9-c/11.4= -((c-4.7)/15.9)
Almost. You messed up the sign.
 
  • #13
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
 

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