Question

Unpolarized light is incident on a system of three ideal polarizers. The second polarizer is oriented at an angle of 30.0° with respect to the first, and the third is oriented at an angle of 45.0° with respect to the first. If the light that emerges from the system has an intensity of 31.8 W/m², what is the intensity of the incident light?

Answer 1

Given:

$\theta_{1}=30^{\circ}=\text{angle between the second polarizer and first polarizer}$

$\theta_{2}=45^{\circ}-30^{\circ}=15^{\circ}=\text{angle between the third polarizer and second polarizer}$

$I=31.8W/m^{2}=\text{intensity of light coming out from the third polarizer}$

1. =? = intensity of unpolarized light

Applying Malus's Law:

The intensity of light coming out from the third polarizer
1 * cos 01 * cos 2
[where $\frac{I_{o}}{2}$ = intensity of light coming out from the first polarizer].

Therefore, after putting the values in the above equation:

1 * cos 01 * cos 2

$\Rightarrow 31.8=\frac{I_{o}}{2}*\cos^{2}30^{\circ}*\cos^{2}15^{\circ}$

$\Rightarrow I_{o}=\frac{2*31.8}{\cos^{2}30^{\circ}*\cos^{2}15^{\circ}}=90.89W/m^{2}$

Therefore, the intensity of incident light is $90.89W/m^{2}$ . [answer]