According to Abbe,in the formula for the resolving power of a microscope,the numerical aperture is represented by:

For a telescope to have large resolving power,the

Two-point white dots are $2 \,mm$ apart on a black paper. They are viewed by an eye of pupil diameter $3 \,mm$. What is the maximum distance at which these dots can be resolved by the eye (in $\,m$)? $(\lambda = 500 \,nm)$

Two stars are $10$ light years away from the Earth. They are seen through a telescope of objective diameter $30\, cm$. The wavelength of light is $600\, nm$. To see the stars just resolved by the telescope,the minimum distance between them should be ( $1$ light year $= 9.46 \times 10^{15}\, m$) of the order of

The aperture of the objective of a telescope is $24.4 \, cm$. What is the resolving power of this telescope if light of wavelength $2440 \, \mathring{A}$ is used to view the object?

The distance of the moon from earth is $3.8 \times 10^5 \text{ km}$. The eye is most sensitive to light of wavelength $5500 \text{ Å}$. The separation of two points on the moon that can be resolved by a $500 \text{ cm}$ telescope will be......$m$.