Question

No sloppy writing, please! I want to be able to see and understand each step :)

The three polarizing filters are bundled so that the polarizing axes of the second and third filters are 33 ° and 71 °, respectively, relative to the polarizing axis of the first filter. Intensity of unpolarized light hitting the bundle after passing through the bundle is 53 W / cm^2. If the intensity of the incoming light is kept constant, what is the intensity of the light passing through the bundle if the second polarizer is removed?

Answer 1

When Unpolarized light of I0 intensity passes through polarizer, then intensity of light will reduced to half (I0/2) and light will be polarized, after that when light passes through 2nd polarizer at angle from first, then

Using Malus's law:

I2 = I1*cos²

I2 = (I0/2)*cos²

Now after that when light passes through 3rd polarizer at angle w.r.t to 2nd polarizer, than

I3 = I2*cos²

I3 = (I0/2)*cos² *cos²

Now given that I3 = 53 W/cm^2

= 33 deg

= 71 - 33 = 38 deg

So,

I0 = 2*I3/(cos² *cos² )

I0 = 2*53/((cos 33 deg)^2*(cos 38 deg)^2)

I0 = 242.7 W/cm^2

Step 2: Now when 2nd polarizer is removed, than after passing through 1st polarizer intensity will be (I0/2)

after that when it passes through 3rd polarizer (now 2nd) then from malus law:

I = (I0/2)*cos²

= angle between both polarizers = 71 deg

So,

I = (242.7/2)*(cos 71 deg)^2

I = 12.9 W/cm^2 = intensity of the light passing through the bundle if the second polarizer is removed

Let me know if you've any query. (See that in which unit you need answer is not mentioned, So I'm using same as the given unit in the final answer, if required units are W/m^2, then use 12.9*10^4 W/m^2)