If a narrow slit of width $2 \, mm$ is illuminated by monochromatic light of wavelength $500 \, nm$,then the distance between the first minima on both sides on a screen at a distance of $1 \, m$ is ....... $mm$.

When a compact disc is illuminated by a source of white light,coloured 'lanes' are observed. This is due to

The phenomenon of diffraction was discovered by ...... .

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?

Red light of wavelength $5400 \ \mathring{A}$ from a distant source falls on a slit $0.80 \ mm$ wide. Calculate the distance between the first two dark bands on each side of the central bright band in the diffraction pattern observed on a screen placed $1.4 \ m$ from the slit. (in $mm$)

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 Å$. If the first diffraction minimum falls at $30^{\circ}$,then the value of $a$ is