with Issues 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)
o
Magnification = f
Where fo is the focal length of the objective fe is the focal length of the eyepiece
e
f
Issues with the use of telescopes Magnification
o
Magnification = f f
e
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
o
f = 600 mm
e
f = 20 mm
Issues with the use of telescopes Magnification
o
Magnification = f f
e
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
o
f = 600 mm
e
f = 5 mm
Issues with the use of telescopes Magnification
o
Magnification = f f
e
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
o
f = 2400 mm
e
f = 20 mm
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
Where
s
D = .25
d is the wavelength of the EM waves being collected in sm (1 sm = 10-6 m)
D is the diameter of the aperture (the opening which collects the wave) in meters The calculated value of s will be in seconds of arc (arc seconds)
d
Issues with the use of telescopes Resolution
smin is called the diffraction limited resolution of the telescope
Issues with the use of telescopes Resolution
min
s (in sm )
D (in m)
(in arc sec)
For the naked eye,
h
= .25
-9 -3
Shortest visible wavelength d400 x 10 m = .4 dm
Diameter of the aperture (the pupil) d 3 mm = 3 x 10 m
min -3
= (0.25) (0.4 ) / (3 x 10 ) 0.33 arc sec
Issues with the use of telescopes Resolution
min
s (in sm )
D (in m) = .25
For the Mount Palomar 200 inch optical telescope, (in arc sec)
-9
s
Shortest visible wavelength d400 x 10 m = .4 dm Diameter of the aperture (the objective) = 200 in = 5.08 m
min (0.25) -2
min
= (0.4 ) / (5.08 ) 1.96 x 10 arc sec
-2 -5 -7
s
s 1.96 x 10 " = 3.2 x 10 ` = 5.5 x 10 degrees
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
s (in sm )
D (in m) = .25
If the Mount Palomar 200 inchsec) telescope recorded radio waves of (in arc optical wavelength 1 meter,
6
s
wavelength d 1 m = 1 x 10 d m Diameter of the aperture (the objective) = 200 in = 5.08 m
min 6 4
= (0.25) (0.1 x 10 ) / (5.08) 4.9 x 10 arc sec
min 4 o
s
s 4.9 x 10 " = 820' = 13.7
Issues with the use of telescopes
Resolutio...