Three polarizing filters are stacked, with the polarizing axis of the second and

Question

Three polarizing filters are stacked, with the polarizing axis of the second and third filters at 24.0° and 60.0°, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 73.0 W/cm2 after it passes through the stack. If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?

w am2 after it pass sthma gh the stack r tha inci Three pola in fire s are stackad, with the nala zin ais t the c ond and third fi rs at 24.09 and 60,0 racoactive , ta that t tha rist. T un intensity is kept constant, what is Intensity or thIlgit arter lt has passed through the stack lf the second polar zer Is removed? 7ed li nt is in dant an the stack the light has intensity 73 nt ant, what is the Inalty er tha lignt

Explanation / Answer

Suppose initial intensity is I0, then after passing through first polarizer

I1 = I0/2

After passing through the second polarizer

I2 = I1*(cos 24 deg)^2 = (I0/2)*(cos 24 deg)^2

After passing through the third polarizer

I3 = I2*(cos (60 - 24) deg)^2 = (I0/2)*(cos 24 deg)^2*(cos 36 deg)^2

given that I3 = 73 W/cm^2, So

I0 = 2*I3/[(cos 24 deg)^2*(cos 36 deg)^2]

I0 = 2*73/[(cos 24 deg)^2*(cos 36 deg)^2]

I0 = 267.29 W/cm^2

Now given that second polarizer is removed. then

I1 = I0/2

I3 = (I0/2)*(cos 60 deg)^2

I3 = (267.29/2)*(1/2)^2 = 33.41 W/cm^2

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