Question

An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter.

(a) What diameter mirror is needed to be able to see 1.00-m detail on a Jovian moon at a distance of 7.50×10⁸km from Earth? The wavelength of light averages 600 nm.
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?

Answer 1

The diameter mirror needed to see 1.00 m detail on a Jovian moon at a distance of 7.50 x 10^8 km from Earth is approximately 732 meters. The result is unreasonable because it requires a mirror diameter much larger than any currently existing telescopes. The assumption that is unreasonable is that it is practical or feasible to build a telescope with such a large diameter mirror.

Step-by-step explanation:

To determine the diameter mirror needed to see 1.00 m detail on a Jovian moon at a distance of 7.50 x 108 km from Earth, we can use the formula for the diffraction limit of a telescope:

d = 1.22 x (wavelength/D)

where d is the smallest detail that can be resolved, wavelength is the average wavelength of light, and D is the diameter of the mirror. Plugging in the values, we have:

D = 1.22 x (600 x 10-9 m) / 1.00 m = 7.32 x 102 m

Therefore, a mirror with a diameter of approximately 732 meters (or a telescope with a mirror of such diameter) would be needed to see 1.00 m detail on a Jovian moon at that distance from Earth.

(b) What is unreasonable about this result? The result is unreasonable because the diameter required for the mirror is much larger than any currently existing telescopes. (c) The assumption that is unreasonable or inconsistent is that it is practical or feasible to build a telescope with such a large diameter mirror.