Two light waves of intensities $I$ and $2 I$ superimpose on each other. If the path difference between the light waves reaching a point is $12.5 \%$ of the wavelength of the light, then the resultant intensity at the point, is (Both the light waves have same wavelength)

The angle between the axes of a polariser and an analyser is $45^{\circ}$. If the intensity of the unpolarised light incident on the polariser is $I$, then the intensity of light emerged from the analyser is

If a slit of width $x$ was illuminated by red light having wavelength $6500\mathop {\rm{A}}\limits^{\rm{^\circ }}$, the first minima was obtained at $\theta=30^{\circ}$. Then, the value of $x$ is

In case of diffraction, if $a$ is a slit width and $\lambda$ is the wavelength of the incident light, then the required condition for diffraction to take place is