Example 23-9 The Hubble Space Telescope
The Hubble Space Telescope (HST) has a circular aperture 2.4 m in diameter. What is the theoretical angular resolution of
the HST for light of wavelength 550 nm?
Set Up
Equation 23-26 gives the angular resolution, the
smallest angular separation of two objects that
can be resolved as a result of diffraction effects.
Solve
We are given l = 550 nm and D = 2.4 m. We
calculate uR from these using Equation 23-26.
Rayleigh’s criterion for resolvability:
l
sin uR = 1.22 (23-26)
D
From Equation 23-26,
1550 * 10-9 m2
= 2.8 * 10-7
12.4 m2
uR = sin21(2.8 * 1027) = 1.6 * 1025 degree
sin uR = 1.22
Reflect
The photograph shown here is a Hubble Space Telescope image of the
minor planet Pluto and its largest moon, Charon. Pluto and Charon are
separated by about 25 * 1025 degrees in this image. They are easily
resolved by HST, for which uR = 1.6 * 1025 degrees. By contrast, a telescope of the same diameter on Earth would have a much poorer resolution
of about 0.03 degrees due to the blurring effects of the atmosphere. Such
a telescope would not be able to resolve Pluto and Charon. This illustrates
one important rationale for orbiting telescopes, which operate high above
the atmosphere.
Pluto
Charon