# Homework Help: 3D Vector Reflection

1. Sep 20, 2012

### jeffto

Hello All,

Let say I have a system of two planar mirrors (M1 and M2), with a known input (I), and a desired output (O2). Here are the parameters:

Azimuth of input: A
Polar of input: B

Azimuth of normal of M1: A+180
Polar of normal of M1: X1 (unknown)

Azimuth of reflected ray from M1: A+180
Polar of reflected ray from M1: X2 (unknown)

Azimuth of normal of M2: X3 (unknown)
Polar of normal of M2: C

Azimuth of reflected ray from M2: D
Polar of reflected ray from M2: E

Where A, B, C, D, and E are known and dependent on the situation.
X1 would be halfway between B and X2 (mirror reflection geometry).

I have tried (still trying) to solve it by using the vector reflection formula and breaking everything down to Cartesian coordinates. The result equations are huge and hard to solve. Lots of trig is involved and it seems like I can't really isolate the unknowns for a few equations.

Before I delve into this method further, I was hoping someone could give me advice on a better method to solve for the unknowns.