Two crossed polarod A and B are placed in the path of a beam of unpolarized light . In between these two polaroid, a third polaroid C is placed such that its principal section is at an angle of `60^@` with that of A. What percentage of intensity of incident unpolarized light emerges from C and B ?

Explanation

Let `I_0` be the intensity of unpolarized light on polaroid A
`thereforeI_A=I_0/2`
`(I_(out))_A=I_0/2`
Polaroids A and B are in crossed position
`therefore(I_B)_A=I_0/2`
Angle between A and C=` theta=60^@`
`(I_(out))_c=(I_(i n))_c= cos^2 theta`
`=I_0/2(cos^2 60^@)=I_0/2 times1/4=I_0/8`

`therefore((I_C)_(out))/((I_0)_(i ncident))=(I_0//8)/I_0=1/8=0.125`
Light transmitted by `C=12.5%`
`(I_C)_(out)=I_0/8` will be the intensity of light incident on B. Angle between A and B=`90^@` and the angle between A and C =`60^@`
`therefore` Angle between C and B `= theta'=30^@`
`therefore(I_B)_(Out)=(I_0/8)(cos^2 theta')`
`therefore(I_B)_(Out)=(I_0/8)(cos^2 30^@)^2=(I_0/8)(sqrt3/2)^2`
`=I_0/8times3/4=(3I_0)/2=0.09375 I_0`
`therefore` Light transmitted by B=9.38%
Result: Intensity of light transmitted by `C=12.5%`
Intensity of light transmitted by `B=9.38%`