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

$A$ light beam of wavelength $800 \,nm$ passes through a single slit and is projected on a screen kept at $5 \,m$ away from the slit. What should be the slit width for the ray optics approximation to be valid (in $\,mm$)?

In a Fraunhofer diffraction pattern,the slit width is $0.2 \ mm$ and the screen is at $2 \ m$ away from the lens. If the distance between the first minimum on either side of the central maximum is $1 \ cm$,the wavelength of light used is: (in $Å$)

Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on

$A$ 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 $mm$?

What is Fresnel distance? Write its formula.