Question

Unpolarized light of intensity $I$ is incident on a system of two polarizes, A followed by $B$. The intensity of emergent light is $I/2$. If a third polarizer $C$ is placed between $A$ and $B$, the intensity of emergent light is reduced to $I/3$. The angle between the polarizers $A$ and $C$ is $\theta$. Then

• A. $\cos \theta ={\left(\frac{2}{3}\right)}^{1/4}$
• B. $\cos \theta ={\left(\frac{1}{3}\right)}^{1/4}$
• C. $\cos \theta ={\left(\frac{1}{3}\right)}^{1/2}$
• D. $\cos \theta ={\left(\frac{2}{3}\right)}^{1/2}$

Answer 1

The correct option is A $\cos \theta ={\left(\frac{2}{3}\right)}^{1/4}$

let initial intensity be $I$.

intensity of the beam after passing through A is $I_1=\frac{I}{2}$

given that intensity after B is $\frac{I}{2}$.

then angle between A and B is zero.

A polariser C is introduced between A and C then by Molus law

after B $I_b=\frac{I}{2}co{s}^2\theta$

and after C $I_c=I_{b}co{s}^2\theta$

so given $I_c=\frac{I}{3}$

from here solving all the three equations $\frac{I}{3}=\frac{I}{2}co{s}^4\theta$

$cos\theta =(\frac{2}{3}{)}^{\frac{1}{4}}$