Corner reflector reflecting light back parallel to incidence

[shaiqbashir]

Hi!

Well can u help me in this problem. it is related to a device called Corner Reflector.

" A corner reflector is formed by three mutually perpendicular reflecting surfaces. Show that a ray of light incident upon the corner reflector (striking all three surfaces) is reflected back along a line parallel to the line of incidence.(Hint: Consider the effect of a reflection on the components of a vector describing the direction of the light ray). The Apollo mission placed this type of reflector on the surface of the moon in 1969."

Please help me in this problem, i just don't know how to solve it. i have only one days left for my test. Plz Help me in detail

"Thanks in advance"

 

[Galileo]

It's easier than you think. Consider reflection from a single plane surface first, say, the xy-plane.
If $\hat r_i=(x,y,z)$ denotes the direction of the incident wave, we know that the reflected ray stays in the same plane of incidence, so the only direction component that changes is the z-component. Since angle of incidence equals angle of reflection, the z-component simply changes sign: $\hat r_i =(x,y,z) \to \hat r_r=(x,y,-z)$.

Consider reflection from a corner as three reflections from 3 plane surfaces.

 

[einstone]

Consider a vector in the direction of a given ray. All you've to note is this- if this ray falls on a surface,the normal component of the vector is reversed &
the other components remain unchanged (a mere re-statement of the law of reflection).
Suppose that initially the vector in the problem is (x,y,z) in the coordinate system formed by the axes where the mirrors meet. In the course of reflections, the components will be changed to their negatives one by one
(for e.g., in the order (-x,y,z)--(-x,-y,z)--(-x,-y,-z) on reflection in the YZ,ZX,XY planes resp.).The negative of a vector is certainly parallel with itself.
Best of luck for the test!
I'm, with great respect,
Einstone.