Question

Assertion: The resolving power of both microscope and telescope depends on the wavelength of light used.
Reason: the resolving power of a lens is the ability to resolve the two images so they are distinctly identified.
A. Both assertion and reason are correct and reason is the correct explanation for assertion
B. Both assertion and reason are correct but reason is not the correct explanation for assertion
C.Assertion is correct but reason is incorrect
D. Assertion is incorrect but reason is correct

Answer 1

Angular separation, $\delta \theta$ = $\dfrac{{1.22\lambda }}{D}$. Even though 200 nanometers is considered the optimal resolution for optical microscopes, higher resolutions can be obtained using fluorescence microscopy. When combined with a laser light source, focal plane resolution of 15-20 nanometers can be achieved.The principal limitation of the light microscope is its resolving power. Using an objective of NA 1.4, and green light of wavelength 500 nm, the resolution limit is ∼0.2 μm. This value may be approximately halved, with some inconvenience, using ultraviolet radiation of shorter wavelengths.

Complete step by step answer:
The resolving power of a microscope is reciprocal of the distance d. An increase in $\mu$(refractive index of the transparent medium between the objects and the objective of the microscope) will produce a greater resolving power. It also increases with decrease in wavelength while the resolving power of the telescope is defined as the reciprocal of the smallest angular separation between two distant objects whose images are distinctly separated by the telescope.
So = $\delta \theta = \dfrac{{1.22\times \lambda }}{D}$
So, for higher resolving power, telescopes should have the objective lens of large diameter (D) and objects illuminated by light of small wavelength. Thus, in both the cases resolving power is increased by taking illumination light of small wavelength.

Note: One must have proper knowledge of resolving power of microscope and telescope to solve these types of questions. The resolving power of a microscope is the most important feature of the optical system and influences the ability to distinguish between fine details of a particular specimen.