The phenomenon of diffraction can be exhibited by

In the diffraction pattern, the first maximum is at $30^{\circ}$, when a monochromatic light of wavelength $\lambda$ is incident on a slit of width $a$. For the same wavelength, if the slit width is changed, so that the first maximum is at $45^{\circ}$, by how much is the slit width changed?

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?

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.

$A$ plane wavefront of wavelength $6 \times 10^{-7} \,m$ is incident on a slit of width $0.4 \,mm$. $A$ convex lens of focal length $0.8 \,m$ is placed behind the slit to form a diffraction pattern on a screen. What is the linear width of the second secondary maximum in $mm$?

The first diffraction minimum due to the single slit diffraction is seen at $\theta = 30^o$ for a light of wavelength $5000 \,\mathring{A}$ falling perpendicularly on the slit. The width of the slit is