The resolving limit of a healthy human eye is about:

$A$ telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength $500 \text{ nm}$, at a resolution of $5 \times 10^{-7} \text{ radian}$. The value of $R$ is . . . . . . $\text{cm}$.

The diameter of the objective lens of a telescope is $250\, cm$. For light of wavelength $600\, nm$ coming from a distant object, the limit of resolution of the telescope is close to:

Two point white dots are $1 \ mm$ apart on a black paper. They are viewed by an eye with a pupil diameter of $3 \ mm$. Approximately,what is the maximum distance at which the dots can be resolved by the eye? (Take wavelength of light $= 500 \ nm$)

$A$ person is observing a bacteria through a compound microscope. For better analysis and to improve the resolving power,he should:

Two points separated by a distance of $0.1\,mm$ can just be resolved in a microscope when a light of wavelength $6000\ \mathring{A}$ is used. If the light of wavelength $4800\ \mathring{A}$ is used,this limit of resolution becomes.......$mm$.