Solve this:
Q.9. Define the term 'linearly polarised light'. When does the intensity of transmitted become maximum, if a polaroid sheet rotated between two crossed polaroids?

Linear polarized and plane polarized is same. Light is considered to be "linearly polarized" when it contains waves that only fluctuate in one specific plane.

There are only 3 kinds of polarizations :

(i) linear or plane polarization

(i) circular polarization.

(iii) elliptical polarization

One passing through first polaroid. the intensity of light becomes half (I/2)

$$\begin{gathered} Let the rotating polaroid sheet makes an angle \theta with the first polaroid. \\ So angle with the other polaroid will be \left(90-\theta \right) \\ Let the intensity from first polaroid is I_o then by malus law the intensity by \\ polaroid P_2 \\ I\text{'}=I_o{\cos }^2\theta \\ and by third polaroid P_3 \\ I\text{'}\text{'}=\left(I_o{\cos }^2\theta \right){\cos }^2\left(90-\theta \right) \\ I\text{'}\text{'}=\frac{I_o}{4}{\sin }^{2}2\theta \\ transmitted intensity will be maximum when {\sin }^{2}2\theta =1 \\ {\sin }^{2}2\theta ={\sin }^2\frac{\pi }{2} \\ 2\theta =\frac{\pi }{2} \\ \theta =\frac{\pi }{4} \end{gathered}$$

Regards