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April 18, 2014

April 18, 2014

Posted by **Knights** on Friday, February 22, 2013 at 2:29pm.

Help?? Won't the laser bounce around until infinity?

- Help please with reflection problem!? -
**Reiny**, Friday, February 22, 2013 at 4:06pmNo, the laser follows the old billiard table rule, that the angle of incidence is the angle of reflection.

I am going to enlarge your square to a 4 by 4, thus making your first bounce BP = 3

make a reasonable sketch, graph paper might be a good idea.

From P it will bounce and hit CD at Q

look at triangles ABP and PCQ, they are both right-angles and similar.

BP^2 + AB^2 = AP^2

9 + 16 = AP^2

AP = √25 = 5

So each triangle formed by a bounce will have the ratio

3:4:5

We are interested in the sum of the paths formed by the hypotenuses

in the second triangle PC, the short side is 1

so by ratios,

PQ/5 = 1/3

PP = 5/3

find CQ by ratios, then you can find QD

On my diagram, I have the following paths:

From A to P ---- 5 units

from P to Q on CD --- done : 5/3 units

from Q to R on AD , R is close to D,

from R to S on BC

from S to T on AB

from T to U on AD and ahhhh

from U to C , which is a vertex.

At this point you should notice that there is a lot of symmetry

and AP = RS = UC

PQ = TU

QR = TS

so once you have found QR, again by using the ratios 3:4:5

you have found the 3 different path lengths

Add up the 7 lengths, don't forget to divide by 4 , my original step to avoid some initial fractions.

- Help please with reflection problem!? -
**Knights**, Friday, February 22, 2013 at 4:50pmThank you very much it helps a lot!!

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