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 wavelengths of light used in an optical instrument are ${\lambda _1 = 4000 \ \text{\AA}}$ and ${\lambda _2 = 5000 \ \text{\AA}}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:

The limit of resolution of a telescope is $2.5 \times 10^{-7} \text{ rad}$. If the telescope is used to detect light of wavelength $500 \text{ nm}$ coming from a star, the diameter of the objective lens used by the telescope is: (in $\text{ cm}$)

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 $5000 \, \mathring{A}$.

$A$ telescope uses light having a wavelength of $5000 \, \mathring{A}$ and lenses with focal lengths of $2.5 \, \text{cm}$ and $30 \, \text{cm}$. If the diameter of the aperture of the objective is $10 \, \text{cm}$,what are the resolving limit and the magnifying power of the telescope,respectively?

The human eye has an approximate angular resolution of $\phi = 5.8 \times 10^{-4} \, rad$ and a typical photoprinter prints a minimum of $300 \, dpi$ (dots per inch, $1 \, inch = 2.54 \, cm$). At what minimal distance $z$ should a printed page be held so that one does not see the individual dots?