Assume that light of wavelength $600\, nm$ is coming from a star. The limit of resolution of a telescope whose objective has a diameter of $2\, m$ is $......... \times 10^{-7}\, rad$.

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

$A$ microscope objective gathers light over a cone of semi-vertex $30^o$ and uses visible light of wavelength $5500 \text{ Å}$. Its resolving limit is

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:

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

The limit of resolution of an oil immersion objective microscope of numerical aperture $0.8$ for light of wavelength $0.6 \mu m$ is