Determine whether a telescope with an objective lens of diameter $20\mathrm{cm}$ can resolve two objects a distance of $10\mathrm{km}$ away separated by $1\mathrm{cm}$. (Assume we are using a wavelength of $600\mathrm{nm}$)

The headlight of a car is separated by a distance of $1.4\mathrm{m}$.

a. Estimate the distance these would be resolved as two separated sources by a lens of the diameter of $5\mathrm{cm}$ with a wavelength of $500\mathrm{nm}$.

b. Discuss the effect, if any, of decreasing the wavelength on the distance in a.

Assume that the pupil of the human eye has a diameter of $4.00\mathrm{mm}$ and receives the light of wavelengths $5.0\times {10}^{-7}\mathrm{m}$.

a. Calculate the smallest angular separation that can be resolved by the eye at this wavelength.

Assume that the pupil of the human eye has a diameter of $4.00\mathrm{mm}$ and receives the light of wavelengths $5.0\times {10}^{-7}\mathrm{m}$.

b. Estimate the least distance between features on the Moon (a distance of $3.8\times {10}^8 \mathrm{m}$away) that can be resolved by the human eye.

The Jodrell Bank radio telescope in Cheshire, UK, has a diameter of $76\mathrm{m}$. Assume that it receives the electromagnetic waves of wavelength $21\mathrm{cm}$.

a. Calculate the smallest angular separation that can be resolved by this telescope.

The Jodrell Bank radio telescope in Cheshire, UK, has a diameter of $76\mathrm{m}$. Assume that it receives the electromagnetic waves of wavelength $21\mathrm{cm}$.

b. Determine whether this telescope can resolve the two-star of a binary star system that is separated by a distance of $3.6\times {10}^{11}\mathrm{m}$ and are $8.8\times {10}^{16}\mathrm{m}$ from earth. (Assume the wavelength of $21\mathrm{cm}$)