Can someone help me explain this and have calculations? Thanks : ) Suppose a bea

Question

Can someone help me explain this and have calculations? Thanks : )

Suppose a beam of light is a mixture of two beams, each polarized. Further suppose the electric fields for the two component beams can be written as
E1 = E0cos(kx-wt)y and
E2 = E0cos(kx-wt+pi/2)z.
Here y and z are unit vectors. (a) Show that for a fixed point, say x = 0, the electric field vector for the total beam sweeps out a circle in the yz plane as time passes. The beam is said to be circularly polarized.
Repeat the calculation when the phase shift is pi instead of pi/2.

Explanation / Answer

case(1), for x=0, E1=cos(wt)y, E2=sin(wt)z and as y and z are unit vectors their magnitude is one. therefore, E1^2 + E2^2 = sin^2(wt).z^2 + cos^(wt).y^2 =1, which is an equation circles in yz plane centred at origin and radius 1 unit. case(2), for x=0, E1=cos(wt)y, E2=cos(wt)z, elemenating cos(wt), E1/E2=1, => E1=E2, which is an equation of line in yz plane passing through origin and slope 45 degree.

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