$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to:

$A$ slit of width $d$ is illuminated by white light. The first minimum for red light $(\lambda = 6500\,\mathring{A})$ will fall at $\theta = 30^\circ$ when $d$ will be

Diffraction effects are easier to notice in the case of sound waves than in the case of light waves because

Yellow light is used in a single slit diffraction experiment with a slit width of $0.6 \, mm$. If the yellow light is replaced by $X$-rays,then the pattern will reveal:

Assertion : When a tiny circular obstacle is placed in the path of light from some distance,a bright spot is seen at the centre of the shadow of the obstacle.
Reason : Destructive interference occurs at the centre of the shadow.

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.