The limit of resolution of a telescope and a microscope is imposed because of which phenomenon?

$A$ Fraunhofer diffraction pattern due to a narrow slit is obtained on a screen placed at a distance $D$ from the slit whose slit width is $a$. The distance of the first secondary maximum from the central maximum is

In a Fraunhofer diffraction of a single slit, when a slit is illuminated by a light of wavelength $6480 \text{ Å}$, the angular width of the central maximum is measured. When the slit is illuminated by light of another wavelength '$\lambda$',the angular width decreases by $25\%$. The value of '$\lambda$' in $\text{Å}$ is:

In a Fraunhofer diffraction pattern,the slit width is $0.5 \ mm$ and the screen is at $2 \ m$ away from the lens. If the wavelength of the light used is $5500 \ Å$,then the distance between the first minima on either side of the central maximum is (assume $\theta$ is small and measured in radians). (in $mm$)

If the slit width is $2 \, mm$ and the wavelength of light used is $4000 \, Å$, then the Fresnel distance is nearly:

$A$ plane wavefront of wavelength $6000 \, \mathring A$ is incident on a slit of width $0.2 \, mm$. $A$ Fraunhofer diffraction pattern is obtained on a screen at a distance of $2 \, m$ from the slit. What is the width of the central maximum in $mm$?