Question

Prof. Marcia Grail, supervillain and superscientist, wishes to spy on her foes (they'll all pay!) from orbit. She wishes to be able to resolve detail on order the size of the letters on a license plate (approx. 5cm), in a wavelength of approximately 550 nm, from an orbit approximately 4.2 x 10^7 m above the surface of the Earth. If her resolution is limited only by diffraction, then what is the smallest aperture telescope that she can get away with

Answer 1

Answer:

563.64 m

Explanation:

Given that as per the question

x = 5 cm = 0.05 m

D = 4.2 × 107 m

d = smallest aperture size

As per the situation the solution of the smallest aperture telescope that she can get away with is below :-

We will use Rayleigh's diffraction limit which is

$d\frac{x}{D} = 1.22\lambda$

The equation will be

$d\frac{0.05}{4.2\times 10^7} = 1.22[550\times 10^{-9}]$

d = 563.64 m

So, the answer is d = 563.64 m