The angular resolution of a $10 \;cm$ diameter telescope at a wavelength of $5000 \;\mathring A$ is of the order of:

We use a simple microscope to magnify an object. The microscope has a numerical aperture of $\sin \alpha = 0.24$. The object is so small that the resolving power of the microscope is fully utilized. If the diameter of the eye's pupil is $d = 4.0 \ mm$ and the least distance of distinct vision is $D = 25 \ cm$,what is the minimum magnifying power of the microscope?

$A$ telescope of aperture $3 \times 10^{-2} \, m$ diameter is focused on a window at $80 \, m$ distance fitted with a wire mesh of spacing $2 \times 10^{-3} \, m$. Given: $\lambda = 5.5 \times 10^{-7} \, m$,which of the following is true for observing the mesh through the telescope?

Light of wavelength $\lambda$ is coming from a star. What is the limit of resolution of a telescope whose objective has diameter $r$?

When the object is self-luminous,the resolving power of a microscope is given by the expression

For a given wavelength,telescopes with large aperture objectives are used for: