Question

two polaroids p1 and p2 are placed with their pass axes perpendicular to each other unpolarised light of intensiy i not is incident onp1 . a third polaroid p3 is kept in between p1 and p2 such that its pass axis makes an angle of 30 degree with that of p1 determine the intensity of light transmitted through p1 p2 and p3 why in this angle between p3 and p2 is taken 30 in solution and whats the differenc if polaroids placed in a way - crossing each other ans soon as possible

Answer 1

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Answer 2

Given that,

Angle = 30°

Polaroids = P₁

Polaroids = P₂

Intensity of unpolarised light = I₀

$I_{0}$ is incident on $P_{1}$

We know that,

Intensity of light is

$I=I_{0}\cos^2\theta$

Where,

I= Intensity of transmitted light after polarization.

I₀ = Intensity of incident light.

Intensity of light after falling on P₁ $I'=\dfrac{I_{0}}{2}$

We need to calculate the intensity of light after falling on P₃

Using formula of intensity

$I''=I'\cos^{2}\theta$

Put the value into the formula

$I''=\dfrac{I_{0}}{2}\cos^2(30)$

$I''=\dfrac{I_{0}}{2}(\dfrac{\sqrt{3}}{2})^2$

$I''=\dfrac{3I_{0}}{8}$

We need to calculate the intensity of light after falling on P₂

Using formula of intensity

$I'''=I''\cos^{2}\theta$

Put the value into the formula

$I'''=\dfrac{3I_{0}}{8}\cos^2(60)$

$I''=\dfrac{3I_{0}}{8}(\dfrac{1}{2})^2$

$I''=\dfrac{3I_{0}}{32}$

Hence, The intensity of light after falling on P₂ is $\dfrac{3I_{0}}{32}$ The intensity of light after falling on P₃ is $\dfrac{3I_{0}}{8}$