Assume that light of wavelength $6000\,\mathring{A}$ is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of $100\,\text{inch}$?

Two luminous point sources separated by a certain distance are at $10 \,km$ from an observer. If the aperture of his eye is $2.5 \times 10^{-3} \,m$ and the wavelength of light used is $500 \,nm$, the distance of separation between the point sources just seen to be resolved is (in $\,m$)

$A$ microscope has an objective of aperture $8 \text{ mm}$ and focal length of $5 \text{ cm}$. The minimum separation between two objects to be just resolved by the microscope is (wavelength of light used $= 5500 \text{ Å}$) (in $\mu\text{m}$)

$A$ telescope is used to observe two objects at a distance of $z = 10 \ km$ which are $s = 0.12 \ m$ apart and illuminated by light of wavelength $\lambda = 600 \ nm$. Estimate the diameter of the objective lens of the telescope if it can just resolve the two objects. Assume diameter $D >> \lambda$ and separation between objects $s << z$. The answer is in $cm$.

The resolving power of a microscope depends upon:

$A$ microscope was initially placed in air (refractive index $1$). It is then immersed in oil (refractive index $2$). For a light whose wavelength in air is $\lambda$,calculate the change of the microscope's resolving power due to oil and choose the correct option.