The diameter of the objective of a telescope is $10 \, cm$. There are two objects at a distance of $1 \, km$ from it. What should be the minimum distance between these two objects so that their images are seen as separate by this telescope? The wavelength of light is $5000 \, \mathring{A}$.

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:

Our eyes are sensitive to the wavelength range of .......

We use a simple microscope to magnify an object. The microscope has a numerical aperture of $\sin \alpha = 0.24$. The object is so small that the resolving power of the microscope is fully utilized. If the diameter of the eye's pupil is $d = 4.0 \ mm$ and the least distance of distinct vision is $D = 25 \ cm$,what is the minimum magnifying power of the microscope?

According to Abbe,in the formula for the resolving power of a microscope,the numerical aperture is represented by:

When the wavelengths of light used in optical instruments $A$ and $B$ are $4500 \, \text{Å}$ and $6000 \, \text{Å}$ respectively, the ratio of the resolving power of $A$ to $B$ will be: