The limit of resolution of a telescope is $2.5 \times 10^{-7} \text{ rad}$. If the telescope is used to detect light of wavelength $500 \text{ nm}$ coming from a star, the diameter of the objective lens used by the telescope is: (in $\text{ cm}$)

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

With the help of a telescope that has an objective of diameter $200 \,cm$, it is proved that light of wavelengths of the order of $6400 \text{ Å}$ coming from a star can be easily resolved. Then, the limit of resolution is

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?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: An electron microscope can achieve better resolving power than an optical microscope.
Reason $R$: The de Broglie wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light.
In the light of the above statements, choose the correct answer from the options given below:

In an optical instrument,the wavelengths of light used are $\lambda_1 = 4000 \ \mathring{A}$ and $\lambda_2 = 5000 \ \mathring{A}$. What is the ratio of their resolving powers?