Two plane polarized light waves combine at a certain point whose electric field components are

$$\begin{aligned} & E_1=E_0 \operatorname{Sin} \omega t \\ & E_2=E_0 \operatorname{Sin}\left(\omega t+\frac{\pi}{3}\right) \end{aligned}$$

Find the amplitude of the resultant wave.

Two polarisers $P_1$ and $P_2$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $P_3$ is inserted in between $P_1$ and $P_2$, at particular angle between $P_2$ and $P_3$. The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers $P_2$ and $P_3$ is :

In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :