Question

The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 89 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 13 cm across. Assume first that object resolution is determined entirely by Rayleigh's criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 414 km and that the wavelength of visible light is 542 nm. What would be the required diameter of the telescope aperture for (a) 89 cm resolution and (b) 13 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b), i.e. is the military surveillance resolution accomplished?

Answer 1

Step-by-step explanation:

minimum angle that can be resolved is given by the expression

1.22 λ / D , λ is wavelength of light , D is aperture of telescope.

distance that can be resolved = d x 1.22 λ / D

d is the distance by which observation is being made.

a )

89 x 10⁻² = 1.22 x 542 x 10⁻⁹ x 414 x 10³ / D₁

D₁ = 30.76 cm

b )

13 x 10⁻² = 1.22 x 542 x 10⁻⁹ x 414 x 10³ / D₂

D₂ = 2.1 m

c ) Hubble space telescope diameter is 2.4 m which is more than that of military surveillance telescope . Since diameter increases the power of resolution , it is capable of resolving two points situated even less than 13 cm apart . But , due to atmospheric turbulence , this power may not be achieved .