$A$ screen is placed at $50 \ cm$ from a single slit,which is illuminated with light of wavelength $600 \ nm$. If the separation between the $1^{st}$ and $3^{rd}$ minima in the diffraction pattern is $3 \ mm$,then the slit width is: (in $mm$)

$A$ parallel beam of light of wavelength $6000 \text{ Å}$ is diffracted by a single slit of width $0.3 \text{ mm}$. The angular position of the first minima of the diffracted light is

Answer the following questions:
$(a)$ In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?
$(b)$ In what way is diffraction from each slit related to the interference pattern in a double-slit experiment?
$(c)$ When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?
$(d)$ Two students are separated by a $7 \; m$ partition wall in a room $10 \; m$ high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily?
$(e)$ Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?

Light of wavelength $5000 \, \text{Å}$ is incident on a slit of width $0.1 \, \text{mm}$. Find the width of the central bright fringe on a screen placed at a distance of $2 \, \text{m}$ in $\text{mm}$.

Explain diffraction by a single slit.

Due to which optical phenomenon do we not see the shadow of an opaque object clearly?