Three identical polaroid sheets P_{1}, P_{2} and P_{3} are oriented so that the pass axis of P_{2} and P_{3} are inclined at angles of 60° and 90° respectively with the pass axis of P_{1}. A monochromatic source S of unpolarised light of intensity I_{0} is kept in front of the polaroid sheet P_{1} as shown in the figure. Determine the intensities of light as observed by the observer at O, when polaroid P_{3} is rotated with respect to P_{2} at angles θ = 30° and 60°.

#### Solution

The ray of light passing through polaroid P_{1} will have intensity reduced by half.'

`I_1=I_0/2`

Now, the polaroid P_{2} is oriented at an angle 60° with respect to _{P1.}

Therefore_{,} the intensity is

`I_2=I_1cos^2 60=I_0/2xx1/4=I_0/8`

Now, the polaroid P_{3} is originally oriented at an angle 90 − 60 = 30°. Hence, when P_{3} is rotated by 30°, the angle between P_{2} and P_{3} is 60°. Therefore, the intensity is

`I_3=I_2cos^2 60=I_0/8cos^2 60=I_0/8xx1/4=I+0/32`

Similarly, when P_{3} is rotated by 60°, the angle between P_{2} and P_{3} is 90°.

Therefore, the intensity is `I_3=I_2cos^2 90=I_0/8xx0xx0`