Question

Unpolarised light is passed through a polaroid $P_1$. When this polarised beam passes through another polaroid $P_2$ and if the pass axis of $P_2$ makes angle $\theta$ with the pass axis of $P_1$, then write the expression of intensity for the polarised beam passing through $P_2$. Draw a plot showing the variation of intensity when $\theta$ varies from $0$ to $2\pi$.

Answer 1

According to the Law of malus, when a beam of completely plane polarised light is incident on the analyser, resultant intensity of light(l) transmitted from the analyser varies directly as the square of the cosine of angle $\theta$ between the plane of analyser and polariser.

i.e., $I\propto {\cos }^2\theta$

or, $I=I_0{\cos }^2\theta$

When unpolarized light passes through P${}_1$:

Ass we know the average value of "${\cos }^2\theta$" (from 0 to $2\pi$)=$\frac{1}{2}$

So using law of malum, $I=I_0{\cos }^2\theta =\frac{I_0}{2}$ [as the intensity get reduced by $\frac{1}{2}$]

Now when polarised light (from P${}_1$) passes through P${}_2$"

When the light which we get from P${}_1$, passes through P${}_2$ its intensity is again given bu maum law,

$I=I_0{\cos }^2\theta$

Now here, the initial intensity is '$\frac{I_0}{2}$'. So, $I=\frac{I_0}{2}{\cos }^2\theta$

now we will plot the graph for this intensity by taking values of '$\theta$' from (0 to 2$\pi$), (the graph is as shown above)