1) Randomly polarized light of intensity Io is passes through two polarizers who

Question

1) Randomly polarized light of intensity Io is passes through two polarizers whose transmission axes differ by

45 degrees. What is the intensity of the light that has passed through both polarizers?

I know the answer is .25. But I don't know how to get there

2) Plane polarized light of intensity Io is sent through a polarizer rotated 45 degrees clockwise to the original plane of polarization and then through a second polarizer rotated by 45 degrees counter-clockwise measured from the original plane of the polarization. What is the transmitted intensity?

3) Light from an astronomical source is found to be shifted to a one percent lower frequency than had the source been at rest. What radial velocity could cause such a shift?

Thank you!!

Explanation / Answer

3)

the relativistic doppler factor is

Fs/F0 = sqrt[(1-beta)/(1+beta)]

where beta = v/c

Fs= 99%*F0 =0.99*F0

(1-beta)/(1+beta) =0.9801

1- beta = 0.9801 +0.9801*beta

0.0199 =1.9801*beta

beta =0.010049997

V = c*beta

V = 3.015*10^6 m/s

The shift is toward lower frequencies (red shift), it means the source is moving away from the observer.

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