Question

In the figure below initially unpolarized ight is sent into a system of three polarizing sheets whose polarizing directions make angles of θί intensity is transmitted by the system? (Hint: Be careful with the angles.) 2-B3 320 with the direction of the y axis. what percentage of the init 82

Answer 1

for the first sheet :

I_o = incident intensity of unpolarized light

I₁ = intensity of polarized light from first sheet

I₁ = I_o/2                                    since light is unpolarized

for the second sheet :

I₁ = intensity of incident polarized light from first sheet = (0.5) I_o

I₂ = intensity of polarized light from second sheet

$\theta$ = angle between first and second sheet = $\theta$ ₁ + $\theta$ ₂ = 32 + 32 = 64 deg

using the equation

I₂ = I₁ Cos² $\theta$

I₂ = I₁ Cos² 64

I₂ = (0.192) (0.5) I_o

I₂ = (0.096) I_o

for the third sheet :

I₂ = intensity of polarized light from second sheet = (0.096) I_o

I₃ = intensity of polarized light from third sheet = ?

$\theta$ ' = angle between first and second sheet = $\theta$ ₃ + $\theta$ ₂ = 32 + 32 = 64 deg

using the equation

I₃ = I₂ Cos² $\theta$

I₃ = I₂ Cos² 64

I₃ = ((0.096) I_o ) Cos² 64

I₃ = (0.018) I_o

I₃ /I_o = (0.018) (100) = 1.8%