Two light waves travel parallel to each other and have electric fields which are

Question

Two light waves travel parallel to each other and have electric fields which are polarized in the y-direction. The electric field from each light ray at some time is E(1y)= E(0)cos(kx+pi), E(2y)= E(0)cos(Kx). Where k=2pi/wavelength, E(0)=1000N/C and wavelength=.50m. Draw a picture of the two interfering light waves so one wave is drawn right above the other wave, find the sum of the electric fields from the two light waves, and explain what the measured intensity of the sum of the two light waves would be.

Explanation / Answer

The two electric fields can be written as

E1= 1000 cos (4pix + pi)

E2= 1000 cos(4pix) since k= 2pi/wavelength

Their vector sum E1+E2= 1000[cos(4pix) + cos(4pix +pi)]

We know that cos(x+pi)= -cos x

Hence the sum is= 1000[cos 4pix - cos 4pix)=0

Intensity is the square of modulus of electric fiels, hence if E is 0, Intensity also is zero

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