Answer to Question #92399 in Optics for James Walker

Question

A mixture of polarised & unpolarised is incident on a polariser. As the polariser is rotated through 360°, it is found that the minimum & maximum of the transmitted intensity is in the ratio 1:q. The ratio of intensities of polarised to unpolarised light in the incident beam is =?

Answer 1

In the case of an unpolarized light beam, 50% of the flux always passes through the polarizer

$$I_1=I_{10}\cdot 0.5$$

In the case of a polarized light beam, its intensity varies according to the Malus law:

$$I_2=I_{20}\cos^2(\phi)$$

Then the maximum and minimum of the past intensity:

$$I_{max}=\frac{I_{10}}{2}+I_{20}\\ I_{min}=\frac{I_{10}}{2}$$

Knowing their relationship, we find:

$$\frac{1}{q}=\frac{\frac{I_{10}}{2}}{\frac{I_{10}}{2}+I_{20}}=\frac{I_{10}}{I_{10}+2I_{20}}\\ I_{10}+2I_{20}=qI_{10}\\ 2I_{20}=(q-1)I_{10}\\ \frac{I_{10}}{I_{20}}=\frac{2}{1-q}$$