The resolving power of a microscope depends upon:

If an object kept at the least distance of distinct vision is just resolved with light of wavelength $500 \ nm$ and a pupil of diameter $1 \ mm$,at what distance will the object be just resolved if the wavelength is $400 \ nm$ and the pupil diameter is $0.8 \ mm$ (in $cm$)?

The diameter of a human eye lens is $2\,mm$. What will be the minimum distance between two points to resolve them,if they are situated at a distance of $50\,m$ from the eye? The wavelength of light used is $5000\,\mathring{A}$.

Explain the resolving power of optical instruments and explain the resolving power of telescopes.

$A$ telescope uses light having a wavelength of $5000 \, \mathring{A}$ and lenses with focal lengths of $2.5 \, \text{cm}$ and $30 \, \text{cm}$. If the diameter of the aperture of the objective is $10 \, \text{cm}$,what are the resolving limit and the magnifying power of the telescope,respectively?

The human eye has an approximate angular resolution of $\theta = 5.8 \times 10^{-4} \text{ rad}$ and a typical photo printer prints a minimum of $300 \text{ dpi}$ (dots per inch, $1 \text{ inch} = 2.54 \text{ cm}$). At what minimal distance $d$ should a printed page be held so that one does not see the individual dots (in $\text{ cm}$)?