A ray represented by a unit vector u ,is reflected by a plane mirror,whose normal is given by another unit vector v,the reflected ray is along unit vector w. Express w in terms of v,u
-
UP 0 DOWN 0 0 2
2 Answers
11
ANGLE OF INCIDENCE=ANGLE OF REFRACTION
v=w+(-u)/|w-v| ...................(1)
( because v is the angle bisector and it will be in the same direction dividing in the same ratio)
|w-v|=OC=2OP
=2|w|cosθ=2cosθ (w is a unit vector)
substituting in eq 1 we get
v=w-u/2cosθ
2vcosθ=w-u
cosθ=-u.v (because u and v are unit vectors)
so
2v(-u.v)=w-v
w=v-2v(v.w)
