IB HL Physics Resolution

Image resolution is a poorly understood topic in IB HL Physics. A tutorial sheet is given below.

1. A double star is examined through a telescope. The stars appear too close together to be resolved. To resolve the image of the stars a coloured filter is placed in front of the telescope. Which coloured filter could allow the images to be resolved? Red or violet?
2. Two stars are observed through a telescope and appear too close together to be resolved. Does increasing the magnification of the telescope resolve the images?
3. The headlights of a stationary car subtend an angle of 1" at a distant point. The human eye can distinguish between two images that are 1' apart. If the wavelength of the light is 550 nm, determine the minimum diameter of a telescope that can allow the headlights to be resolved as separate images.
4. A satellite is in orbit 350 km above the surface of the Earth. Newspint has a size of 3.0 mm. Determine the diameter of the aperture of a camera in the satellite that will allow a newspaper on the Earth to be read from orbit in light of wavelength (a) 600 nm, (b) 400 nm. The resolution of the human eye is 1'.
5. If we increase the amount of light entering a telescope, keeping the diameter and the wavelength constant, does this improve the image resolution? Why?