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Issues with the use of telescopes
Magnification
Magnification determines how much larger the image is as compared to
the size of the source of the light (the object)
Magnification =
fo
fe
Where
fo is the focal length of the objective
fe is the focal length of the eyepiece
Issues with the use of telescopes
Magnification
Magnification =
fo
fe
A cheap telescope has an objective focal length of 600 mm, an objective
diameter of 0.05 m and an eyepiece focal length of 20 mm. What is the
magnification of this telescope?
Given
fo = 600 mm
fe = 20 mm
D = 0.05 m
M = 600 mm / 20 mm = 30
Issues with the use of telescopes
Magnification
Magnification =
fo
fe
A cheap telescope has an objective focal length of 600 mm , an objective
diameter of 0.05 m and an eyepiece focal length of 5 mm. What is the
magnification of this telescope?
Given
fo = 600 mm
fe = 5 mm
D = 0.05 m
M = 600 mm / 5 mm = 120
Issues with the use of telescopes
Magnification
Magnification =
fo
fe
An expensive telescope has an objective focal length of 2400 mm , an
objective diameter of 0.2 m and an eyepiece focal length of 20 mm. What is
the magnification of this telescope?
Given
fo = 2400 mm
fe = 20 mm
D = 0.2 m
M = 2400 mm / 20 mm = 120
Issues with the use of telescopes
Magnification
Question: Is the cheap telescope with a 5 mm eyepiece
as good as the expensive telescope with a 20 mm
eyepiece?
What do you think?
Issues with the use of telescopes
Resolution
More important (possibly more important) than magnification is resolution.
Resolution – the property of an instrument to identify (resolve) small details.
The smallest angular size identifiable by an instrument is given by
min = .25
Where

D
 is the wavelength of the EM waves being collected in m (1 m = 10-6 m)
D is the diameter of the aperture (the opening which collects the wave) in
meters
The calculated value of  will be in seconds of arc (arc seconds)
Issues with the use of telescopes
Resolution
min is called the diffraction limited
resolution of the telescope
Issues with the use of telescopes
Resolution
min (in arc sec) = .25
 (in m )
D (in m)
For the naked eye,
Shortest visible wavelength 400 x 10-9 m = .4 m
Diameter of the aperture (the pupil)  3 mm = 3 x 10-3 m
θmin = (0.25) (0.4 ) / (3 x 10-3 ) ≈ 0.33 arc sec
min  33” = .55’ = .0093o
The average human eye can resolve object with an angular diameter of about a
half a minute.
Issues with the use of telescopes
Resolution
min (in arc sec) = .25
 (in m )
D (in m)
For the Mount Palomar 200 inch optical telescope,
Shortest visible wavelength 400 x 10-9 m = .4 m
Diameter of the aperture (the objective) = 200 in = 5.08 m
θmin = (0.25) (0.4 ) / (5.08 ) ≈ 1.96 x 10-2 arc sec
min  1.96 x 10-2 “ = 3.2 x 10-5 ‘ = 5.5 x 10-7 degrees
The Mount Palomar telescope can resolve objects about 1700 times smaller
than the naked eye
Issues with the use of telescopes
Resolution – The Hubble Space Telescope
Hubble works on the same principle as the first reflecting telescope built in the 1600s by Isaac
Newton. Light enters the telescope and strikes a concave primary mirror, which acts like a lens
to focus the light. The bigger the mirror, the better the image.
In Hubble, light from the primary mirror is reflected to a smaller secondary mirror in front of the
primary mirror, then back through a hole in the primary to instruments clustered behind the focal
plane (where the image is in focus).
Mirror size
Primary mirror: 2.4 m – (94.5 inches) in diameter
Secondary mirror: 0.3 m - (12 inches) in diameter
Angular resolution
Hubble's angular resolution is 0.05 arcsecond. This is the "sharpness" of Hubble's vision. If
you could see as well as Hubble, you could stand in New York City and distinguish two
fireflies, 1 m (3.3 feet) apart, in San Francisco.
Issues with the use of telescopes
Resolution
min (in arc sec) = .25
 (in m )
D (in m)
If the Mount Palomar 200 inch optical telescope recorded radio waves of
wavelength 1 meter,
wavelength  1 m = 1 x 106 m
Diameter of the aperture (the objective) = 200 in = 5.08 m
θmin = (0.25) (0.1 x 106 ) / (5.08) ≈ 4.9 x 104 arc sec
min  4.9 x 104 “ = 820’ = 13.7o
The angular diameter of the moon = 30’
The angular diameter of the Andromeda Galaxy  178’
The Mount Palomar telescope would not be able to resolve these objects
It would not be able to “see” the moon !
Issues with the use of telescopes
Resolution
min (in arc sec) = .25
 (in m )
D (in m)
For the National Radio Astronomical Observatory Robert C. Byrd Radio Telescope,
wavelength  1 m = 1 x 106 m
Diameter of the aperture (the objective) = 100 m
θmin = (0.25) (1 x 106 ) / (100 ) ≈ 2500 arc sec
min  2500” = 41’ = .69o
The angular diameter of the moon = 30’
The angular diameter of the Andromeda Galaxy  178’
The NRAO telescope would be able (roughly) to resolve radio sources of
these angular diameters
Issues with the use of telescopes
Resolution
min (in arc sec) = .25
 (in m )
D (in m)
For the Arecibo Radio telescope,
wavelength  1 x 106 m
Diameter of the aperture (the objective) = 305 m
θmin = (0.25) (1 x 106 ) / (305 ) ≈ 819 arc sec
min  819” = 13.7’ = .22o
The angular diameter of the moon = 30’
The angular diameter of the Andromeda Galaxy  178’
The Arecibo telescope would easily be able to resolve radio sources of
these angular diameters
Issues with the use of telescopes
Magnification
Question: Is the cheap telescope with a 5 mm eyepiece as good as the
expensive telescope with a 20 mm eyepiece?
The magnifications in both cases are the same. However, the diffraction
limited resolutions are (using 0.4 μm for the visible wavelength)
Θmin,cheap = (0.25) (0.4) / (0.05) = 2 arc sec
Θmin,expensive = (0.25) (0.4) / (0.2) = 0.5 arc sec
The expensive telescope will resolve objects 4 times smaller than the cheap
telescope. In part, the expense of a larger telescope is related to resolution
more that magnification.