Monochromatic light of wavelength $4800 \mathop {\rm{A}}\limits^{\rm{o}}$ falls on slit of width ' $a$ '. For what value of ' $a$ ', the first maximum falls at $30^{\circ} .\left(\sin 30^{\circ}=0.5\right)$

In Young's double slit experiment, waves from slits ' $\mathrm{S}_1$ ' and ' $\mathrm{S}_2$ ' have a path difference of $\frac{\lambda}{4}$ and $\frac{\lambda}{6}$ respectively at points $x$ and $y$ on the screen. The ratio of intensities at points $y$ to that at $x$ is $\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}, \cos 30^{\circ}=\sqrt{3} / 2,\right)$

' 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