$A$ parallel beam of light of wavelength $500\; nm$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen $1\;m$ away. It is observed that the first minimum is at a distance of $2.5\;mm$ from the centre of the screen. Find the width of the slit. (in $; mm$)

Which of the following are true for a single slit diffraction?
$(A)$ Width of central maxima increases with increase in wavelength keeping slit width constant.
$(B)$ Width of central maxima increases with decrease in wavelength keeping slit width constant.
$(C)$ Width of central maxima increases with decrease in slit width at constant wavelength.
$(D)$ Width of central maxima increases with increase in slit width at constant wavelength.
$(E)$ Brightness of central maxima increases for decrease in wavelength at constant slit width.

The condition for diffraction is

Light of wavelength $5000 \text{ Å}$ is incident normally on a slit. The first minimum of the diffraction pattern is observed to lie at a distance of $5 \text{ mm}$ from the central maximum on a screen placed at a distance of $2 \text{ m}$ from the slit. The width of the slit is: (in $\text{ cm}$)

$A$ circular disc is placed in front of a narrow source. When the point of observation is at a distance of $1 \, m$ from the disc,the disc covers the first $HPZ$ (Half Period Zone). The intensity at this point is $I_0$. The intensity at a point at a distance of $25 \, cm$ from the disc will be:

$A$ screen is placed $0.5 \,m$ away from a single slit which is illuminated by a monochromatic light of wavelength $6000 \text{ Å}$. If the distance between the first and third minima in the diffraction pattern on the screen is $3 \,mm$, then the slit width is: (in $\,mm$)