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 $\,mm$)?

For what distance is ray optics a good approximation when the aperture is $3\; mm$ wide and the wavelength is $500\; nm$?

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by light of wavelength $6000 Å$. If the slit is illuminated by light of another wavelength,the angular separation decreases by $20 \%$. The wavelength of light used is (in $Å$)

Two towers on top of two hills are $40 \, km$ apart. The line joining them passes $50 \, m$ above a hill halfway between the towers. What is the longest wavelength of radio waves (in $cm$),which can be sent between the towers without appreciable diffraction effects?

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