When a ray of light falls on any surface, a part of the light is sent back to the same medium. This phenomenon where the incident light falling on a surface is sent back to the same medium is known as reflection.
This short note gives the equation for a reflected ray.
Given a ray Ri incident at a point on a surface with normal N one wishes to determine the reflected ray from that point.
The result is determined by straightforward geometry as follows where “.” indicates the dot product and typically N and R1 are unit vectors.
Rr = N (R1 . N) + a
R1 + a = N (R1 . N)
Rr = 2 N (R1 . N) – R1
If -Ri is substituted for R1 then we have
Rr = Ri – 2 N (Ri . N)
Some obvious things to note at extreme cases. If Ri is parallel to the normal then Rr = N, that is, the reflected ray is in the opposite direction to the incident ray. If the incident ray is perpendicular to the normal then it is unaffected, Rr = Ri, this is a glancing ray.
Or to put it another way, this is a picture of two shiney vases.
These are part of the treasures on display at Lichfield Cathedral UK
SILVER WARE or SILVER COLLECTIBLES – CROSSES, CRAFTS & COLLECTIBLES
Something Antique/Old and Silver – Everything Old a New Treasure
Everything Old a New Treasure
CROSSES, CRAFTS & COLLECTIBLES