In a diffraction pattern, light of wavelength $580 \,nm$ is incident normally on a slit of width '$a$'. The distance between the slit and the screen is $2.5 \,m$ and the distance of the second-order maximum from the center of the screen is $14.5 \,mm$. The value of '$a$' is:

$A$ parallel beam of fast-moving electrons is incident normally on a narrow slit. $A$ screen is placed at a large distance from the slit. If the speed of the electrons is increased,which of the following statements is $CORRECT$?

In Fraunhofer diffraction by a single slit,if the slit width is $a$,the wavelength is $\lambda$,and the focal length of the lens is $f$,what is the linear width of the central maximum?

If $I_0$ is the intensity of the principal maximum in the single slit diffraction pattern,then what will be the intensity when the slit width is doubled?

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.

Describe the simplest experiments to observe a diffraction pattern.