The diameter of the objective of a telescope is $3.6 \ m$. The limit of resolution of the telescope for a light of wavelength $540 \ nm$ is

$A$ 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?

Two point white dots are $1 \ mm$ apart on a black paper. They are viewed by an eye with a pupil diameter of $3 \ mm$. Approximately,what is the maximum distance at which the dots can be resolved by the eye? (Take wavelength of light $= 500 \ nm$)

Wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \; \mathring{A}$ and $\lambda_2 = 5000 \; \mathring{A}$. The ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is:

The diameter of the objective of the telescope is $0.1 \ m$ and the wavelength of light is $6000 \ \mathring{A}$. Its resolving power would be approximately:

The numerical aperture of a microscope is $0.12$, and the wavelength of light used is $600 \, nm$. Then its limit of resolution will be nearly $............. \, \mu m$.