Question

3 Satellite There are claims that a spy satellite can read license plate numbers from space or read a newspaper over your shoulder. In this problem, we will assess these claims using wave optics. (a) Reading a licence plate number requires a linear resolution of about 5 cm. (You must be able to distinguish objects that are 2 inches apart.) For a satellite at a height of 150 km, what angular resolution does this imply? (b) For light with a wavelength of 550 nm, what size aperture is required to achieve this resolution? (c) Many newspapers use 10 point fonts for the text: The standard size of a letter is about 3.5 mm What size aperture would the same satellite need in order to read the newspaper over your shoulder? (d) Critical Thinking: Are either of these lens sizes feasible? Can a spy satellite can read license plate numbers omspace ar read or ur sbonulder?

I need (c) and (d) answered

Answer 1

(c) Here, we will use Rayleigh criteria

The diameter of lens is given as

d = 1.22 * wavelength * height of satellite / font size

d = 1.22 * 550e-9 * 150,000 / 3.5e-3

d = 28.7 m

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(d) This is a pretty big diameter. The hubble space telescope has a mirror diameter of 4 m which is pretty less.....so, this size is not feasible....yes, if we can make it, then we can read plates and news from space.