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An unpolarised beam of light of intensit...

An unpolarised beam of light of intensity `l_0` falls on a poloroid. The intensity of the emergent beam is

A

`I_0/2`

B

`I_0`

C

`I_0/4`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
A
Proof: Intensity of incident light with amplitude `E_0` is
`I_0 prop E_0^2`………..(1)
Intensity of transmitted light with amplitude `E_0 cos theta` (where `theta`= angle made by incident `vec E` vector with the optic (or pass) axis of a given poloroid) is,
`I prop (E_0 cos theta)^2`
`therefore I prop E_2^ cos^2 theta`..........(2)
Taking ratio of equation (2) to equation (1) `therefore I=I_0 cos^2 theta`
Now, intensity of transmitted beam is the average of above intensity, Hence,
`lt I gt =I_0lt cos^2 theta gt `( `because I_0`= constant)
`therefore lt I gt =I_0(1/2)`
(`because` Incident light in unpolarised and so `theta` varies between 0 to `2pi` and we know average value of `cos^2 theta` over this interval is `1/2`)
`therefore lt I gt =I_0/2`
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