Issues with the use of telescopes

1
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)
fo
Magnification
fe
Where fo is the focal length of the objective
fe is the focal length of the eyepiece
2
Issues with the use of telescopes Magnification
fo
Magnification
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
3
Issues with the use of telescopes Magnification
fo
Magnification
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
4
Issues with the use of telescopes Magnification
fo
Magnification
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
5
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?
6
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
D

• Where
• ? 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)

7
Issues with the use of telescopes Resolution
?min is called the diffraction limited resolution
of the telescope
8
Issues with the use of telescopes Resolution
? (in ?m )
?min (in arc sec) .25
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 ?min (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.
9
Issues with the use of telescopes Resolution
? (in ?m )
?min (in arc sec) .25
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 ?min (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
10
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 sizePrimary mirror 2.4 m (94.5
inches) in diameter Secondary mirror 0.3 m -
(12 inches) in diameter   Angular
resolutionHubble'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.
11
Issues with the use of telescopes Resolution
? (in ?m )
?min (in arc sec) .25
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 ?min
(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 !
12
Issues with the use of telescopes Resolution
? (in ?m )
?min (in arc sec) .25
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 ?min (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
13
Issues with the use of telescopes Resolution
? (in ?m )
?min (in arc sec) .25
D (in m)
For the Arecibo Radio telescope, wavelength ? 1
x 106 ?m Diameter of the aperture (the
objective) 305 m ?min (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
14
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) Tmin,cheap (0.25) (0.4) /
(0.05) 2 arc sec Tmin,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.