# Thread: How to find expression with vectors?

1. ## How to find expression with vectors?

Given unit vectors L (the direction from a surface point P to a point light source) and N (the unit normal to the surface at P), let R be the direction of specular reflection of the point light at P: R is a unit vector that lies in the plane of L and N such that the angle of reflection is equal to the angle of incidence. Find an expression for R in terms of N and L. Im not quite sure how to approach this at all. any help please?

2. The vector L can be broken up into 2 parts, one part parallel to N (L_par) and the other perpendicular to N (L_perp). If you subtract the L_perp from L, then you get L_par. What happens if you subtract 2 * L_perp from L? It may help to draw a triangle diagram.

3. Originally Posted by qmech
The vector L can be broken up into 2 parts, one part parallel to N (L_par) and the other perpendicular to N (L_perp). If you subtract the L_perp from L, then you get L_par. What happens if you subtract 2 * L_perp from L? It may help to draw a triangle diagram.
I dont understand your interpretation of the problem.

4. See attached BMP file.

The first picture shows the light coming in, the normal to the surface, and the light going out. Notice the angle at the point of intersection is the same for the incoming and outgoing light.

The second picture shows how to break down the L vector into a part parallel to N and a part perpendicular to N.

The 3rd picture shows what happens when you subtract 2 L_perp from L. Can you see that this is R?