' n ' polarising sheets are arranged such that each makes an angle $45^{\circ}$ with the proceeding sheet. An unpolarised light of intensity I is incident into this arrangement. The output intensity is I/ 64 . The value of $n$ will be $\left(\cos 45^{\circ}=1 / \sqrt{2}\right)$

In an interference experiment, the phase difference between the waves reaching a first dark point is

In Young's double slit experiment, the intensities at two points, for the path difference $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ are $\mathrm{I}_1$ and $\mathrm{I}_2$ respectively. If $\mathrm{I}_0$ denotes the intensity produced by each one of the individual slits then the ratio $\left(\mathrm{I}_1+\mathrm{I}_2\right): \mathrm{I}_0$ is $\left(\cos 45^{\circ}=1 / \sqrt{2}\right)\left(\cos 60^{\circ}=0.5\right)$

In Young's double slit experiment, fringe width is 1.4 mm with light of wavelength $6000 $$\mathop {\rm{A}}\limits^{\rm{o}} $. If the light of wavelength $5400 $$\mathop {\rm{A}}\limits^{\rm{o}} $ is used, with no other change in the experimental set up. The change in fringe width is