Answer to Question #88054 in Optics for J

Question

Unpolarized light passes through two polaroids, the axis of one is vertical and that of the other is 60 degrees to the vertical. (a) what is the orientation and intensity of the transmitted light. (b) which happens if a third polaroid, with axis 45 degrees to each of the other two, is placed in between

Answer 1

(a) what is the orientation and intensity of the transmitted light

Intensity of the transmitted light is given by

$$ɛ=\frac {I_2-I_1}{I_0} (1)$$

The intensity of a linearly polarized light passing through a polarizer is given by Malus' law:

$$I_2=I_1 \cos^2\theta (2)$$

where

$$I_1=\frac {I_0}{2}$$

We put (2) in (1):

É›=-0.875

Answer:

-0.875 or -87.5%

(b) which happens if a third polaroid, with axis 45 degrees to each of the other two, is placed in between

Intensity of the transmitted light is given by

$$ɛ=\frac {I_3-I_0}{I_0} (3)$$

The intensity of a linearly polarized light passing through a polarizer is given by Malus' law:

$$I_3=I_2 \cos^2(90-\theta) (4)$$

We put (2) and (4) in (3):

É›=-0.905

Answer:

-0.905 or -90.5%