Physics - Wave Optics Question with Solution | TestHub

Intensity of the incident unpolarised light is $I$.

When unpolarised light passes through the first polaroid, the transmitted intensity becomes half of the initial intensity. Thus, the intensity after the first polaroid is:
$I_1=\frac{I}{2}$

According to Malus's law, when polarised light of intensity $I_0$ passes through a polaroid placed at an angle $\theta$ with the plane of polarisation, the transmitted intensity is $I_0{\cos }^2\theta$.

Intensity after passing through the second polaroid:
$I_2=I_1{\cos }^2\theta =\frac{I}{2}{\cos }^2\theta$

Intensity after passing through the third polaroid:
$I_3=I_2{\cos }^2\theta =\frac{I}{2}{\cos }^4\theta$

Intensity after passing through the fourth polaroid:
$I_4=I_3{\cos }^2\theta =\frac{I}{2}{\cos }^6\theta$

Given that $\cos \theta =X$, substituting this into the expression gives:
$I_4=\frac{I{X}^6}{2}$

Answer: $\frac{I{X}^6}{2}$