Incident ray is along the unit vector v and the reflected ray is along the unit vector w . The normal is along unit vector a outwards. Express w in terms of a and v.

Hello Student,

v is unit vector along the incident ray and w is the unit vector along the reflected ray. Hence a is a unit vector along the external bisector of v and w.
w-v=ka
=>1+1+2*cos 2theta =k^2
=>k=2sin theta
where 2θ is the angle between v and w.

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty