Question

In Tolkein's "The Lord of The RIngs" Legolas the elf can accurately count horsemen and discern their hair color from a distance of 5 leagues on a bright, sunny day. Assume one leage is 5km, and that you can distinguish hair color if you resolve the head of a horseman, which has a typical size of 20cm. You may neglect curvature of the earth.

a). Assuming elves have eyes that are optimized for optical light as we see (peak wavelength=5500Å), what diameter must his pupils be to discern this assuming he uses his eyes at the diffraction limit?

b). Calculate the angular size of Venus as observed from Earth for times when Venus is closest and farthest from Earth, and at maximum separation from the Sun. Could our elf friend resolve the phases of Venus?

c). Some species of animal on Earth have adaptations to see at different wavelengths than humans (eg, raindeer use ultraviolet light to find lichen to eat), so it may be safe to assume that elves see differently than humans. Make a plot of what diameter pupils he must have as a function of wavelength, for wavelengths in which the atmosphere is mostly transparent, ie, 3500Å - 2.5μm. +5 points for doing this by computer and not by hand.

Answer 1