In telescopes, for a given wavelength, the objectives with large aperture are used for

The diameter of a human eye lens is $2\,mm$. What will be the minimum distance between two points to resolve them,if they are situated at a distance of $50\,m$ from the eye? The wavelength of light used is $5000\,\mathring{A}$.

The resolving power of an astronomical telescope is $0.2$ seconds. If the central half portion of the objective lens is covered,the resolving power will be......$sec$

The diameter of the objective lens of a microscope makes an angle $\beta$ at the focus of the microscope. Further,the medium between the object and the lens is an oil of refractive index $n$. Then the resolving power of the microscope

For a telescope to have large resolving power,the

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: