Question

If ê₁= unit vector along incident ray,ê₂ = unit vector along reflected ray & n̑=unit vector along normal, then vector form of laws of Reflection is 

a) ê₂=ê₁+2(ê₁. n̑) n̑ 

b) ê₂=ê₁-2(ê₁. n̑) n̑ 

c) ê2=ê₁+(ê₁. n̑) n̑ 

d) ê₂=ê₁-(ê₁. n̑) n̑ 

Answer 1

 From vector law of addition in triangle OPQ 

OP= OQ+QP 

OP ê₂=OQê₁+2QRn̑ 

ê2=ê1+2QR/OP n̑ (OP=OQ) 

sin [(π/2)-i] = cos i = PR/OP = QR/OP 

ê₂=ê₁+2 cos i n̑

Now ê₁.n̑=|݁ê₁||n₁| cos (π-i) = - cos ı̂ 

ê₂=e₁-2(ê₁.n̑) n̑ 

This is vector form of law of reflection.