Que 37: 37 The x-y plane is the boundary between two transparent media Medium -1 with - Physics - Ray Optics and Optical Instruments

Question

Que 37:

37 The x-y plane is the boundary between two transparent media
Medium -1 with z>0 has refractive index 2 and medium -2 with
z<0 has a refractive index 3 A ray of light in medium -1 gien by
the vector A = 6 3 i ^ + 8 8 j ^ - 10 k ^ is incident on the plane
of separation Find the unit vector in the direction of refracted
ray in medium -2

Decoder_2 · Accepted Answer

Dear Student,cosθ1=106(3)2+(83)2+100=1020⇒θ1=60ousing μ1sinθ1=μ2sinθ2 we get,2sin60o=3sinθ2⇒θ2=45ounit vector in thedirection of refracted ray will be given by,63i^+83j^+ak^ so we have,(63i^+83j^+ak^)
k^=63i^+83j^-ak^cos45oa=36×3+64×3+a2×0 707a20
7072=300+a20 293a20 499=300⇒a=22
62so the unit vector is 63i^+83j^+22
62k^36×3+64×3+22 622=128 4863i^+83j^+22 62k^Regards