Physics - Wave Optics Question with Solution | TestHub

Initial intensity of the unpolarized light is $I_0$.

When unpolarized light passes through the first polaroid $P_1$, the intensity becomes half. Thus, the intensity after $P_1$ is:

$I_1=\frac{I_0}{2}$

For each subsequent polaroid $P_k$ ($k=2,3,\dots ,n$), the angle between its pass axis and the plane of polarization of the incident light is $60^{\circ }$.

According to Malus's Law, the intensity after passing through the $k$-th polaroid is:

$I_k=I_{k-1}{\cos }^2(60^{\circ })$

Since $\cos (60^{\circ })=\frac{1}{2}$, we get:

$I_k=I_{k-1}{\left(\frac{1}{2}\right)}^2=\frac{I_{k-1}}{4}$

Applying this relation successively for the remaining $(n-1)$ polaroids, the final intensity $I_n$ is:

$I_n=I_1{\left(\frac{1}{4}\right)}^{n-1}$

Substituting $I_1=\frac{I_0}{2}$:

$I_n=\frac{I_0}{2}{\left(\frac{1}{2^2}\right)}^{n-1}=\frac{I_0}{2\cdot 2^{2n-2}}=\frac{I_0}{2^{2n-1}}$

Answer: $\frac{I_0}{2^{2n-1}}$