Question

An unpolarized light passes through three polarizing sheets whose polarizing directions make an angle of 30°, 60° and 30° with y axis in same sense. What fraction of initial intensity is transmitted by the system ?

Answer 1

Given that,

An unpolarized light passes through three polarizing sheets whose polarizing directions make an angle of 30°, 60° and 30°.

We know that,

The light of intensity is defined as,

$I'=I\cos\theta$

So, the intensity is at first angle

$I_{1}=I\cos30$....(I)

The intensity is at second angle

$I_{2}=I_{1}\cos60$....(II)

The intensity is at third angle

$I_{3}=I_{2}\cos30$...(III)

We need to calculate the initial intensity

Using equation (III)

$I_{3}=I_{2}\cos30$

Put the value of I₂ in the equation

$I_{3}=I_{1}\cos60\cos30$

Put the value of I₁ in the equation

$I_{3}=I\cos30\cos60\cos30$

Put the value in the equation

$I_{3}=I\times\dfrac{\sqrt{3}}{2}\times\dfrac{1}{2}\times\dfrac{\sqrt{3}}{2}$

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

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

Hence, The initial intensity is $\dfrac{8}{3}I_{3}$