Question

A light ray parallel to the x axis strikes the outer reflecting surface of a sphere at a point (2, 2, 0). Its centre is at the point (0, 0,-1). 

Find the unit vector along the direction of reflected ray

(a) (-i+8j+4k)/9 

(b) (i+8j+4k)/9 

(c) (-i+8j-4k)/9 

(d) (-i+-j+4k)/9

Answer 1

If ê1=unit vector along incident ray,ê₂=unit vector along reϐlected ray & n̑=unit vector along normal, then vector form of laws of Reflection is ê₂=e₁-2(ê₁.n̑) n̑  

n̑= (2i+2j+k)/3 

ê₂=? e₁=-i 

Using vector form of laws of Reflection ê₂=e₁-2(ê₁.n̑) n̑ 

ê₂= -i-2(-2/3) (2i+2j+k)/3 = -i+4 (2i+2j+k)/9= (-i+8j+4k)/9