# Math Help - law of reflection

1. ## law of reflection

Two mirrors are placed at a 90° angle to each other. A light ray strikes one mirror 0.650 m from the intersection of the mirrors with an incident angle of 36.5°. The ray then travels a distance d before reflecting from the second mirror. (a) What is the distance d?

please explain how you got the answer to me once you get it because i soooo dont get it! thanks a million!!! ^^

2. Hello, soojin89!

I assume you made a sketch . . .

Two mirrors are placed at a 90° angle to each other.
A light ray strikes one mirror 0.650 m from the intersection of the mirrors
with an incident angle of 36.5°.
The ray then travels a distance $d$ before reflecting from the second mirror.
(a) What is the distance $d$?
Code:
            D
C * - - * - - -
|    /
|   /
0.65 |  /d
|θ/
|/
B *
|\
|θ\
|  \
|   \
|    A

The ray come in from $A$, strikes the first mirror at $B$
. . and reflects to point $D$ on the other mirror.
$BC = 0.65,\;\;\theta = 36.5^o$

In right triangle $BCD\!:\;\;\cos36.5^o \:=\:\frac{0.65}{d} \quad\Rightarrow\quad d \:=\:\frac{0.65}{\cos36.5^o} \;\approx\;0.8086$ m.