Download Optics and Telescopes

Lecture 3
Optics and Telescopes
The Telescopes of Mauna Kea
Guiding Questions
1. 
Why is it important that telescopes be large?
2. 
Why do most modern telescopes use large mirrors
rather than large lens?
3. 
Why are observatories in such remote locations?
4. 
How do astronomers use telescope to measure the
spectra of distance objects?
5. 
Why do astronomers need telescopes that detect radio
waves and other non-visible forms of light?
6. 
Why is it useful to put telescopes in orbit?
Homework 3
FGK10: Chap 5, Q-43, 44; Chap 6, Q-24, 32, 38
NB: for Q-38 in Chap 6, first find HST’s resolution using
information from Question 32.
and
A1: A telescope with an objective focal length of f1, and
an eyepiece focal length of f2. The objective and the
eyepiece are separated by the sum of their focal
lengths f1+f2. Show that the angular magnification of
the telescope is given by f1/f2.
3.1 refracting and reflecting telescopes
•  A lens or mirror changes the
direction of light to
concentrate incoming light
at a focus and form an
image of the light source at
the focal plane.
•  Telescopes using lens are
refractors, and those using
mirrors are reflectors.
A mirror reflects light to form an image.
A lens refracts light to make an image.
A human eye is a lens.
A refracting telescope uses a large diameter objective
lens with a long focal length to form an image and a
small eyepiece lens with a short focal length to magnify
the image.
f2
f1
In modern astronomy, a CCD (charge-coupled device)
camera replaces the eyepiece and is placed at the focal
plane to record observations in digital format.
The largest refractor ever built since 1897, 102 cm (=1.02 m)
diameter , 19.5 m focal length. Housed in Yerkes
Observatory near Chicago.
There are many designs of reflecting telescopes, mostly with a
primary mirror and a secondary mirror.
•  Newtonian focus
•  Prime focus
•  Cassegrain focus
•  Coude focus Gemini North Telescope on
Mauna Kea
Most modern telescopes are reflectors.
Problems with refractors:
•  Chromatic aberration: focal
length varies with wavelength
•  Costly to make a large lens free
of defects, such as bubbles
•  Light is absorbed and scattered in
the glass
•  Heavy to support, distortion under
weight
Chromatic aberration
Advantages of reflectors:
•  The mirror is made to be highly
reflective.
•  Fewer problems with chromatic
aberration, glass defects,
support and distortion.
•  Spherical aberrations can be
corrected.
Spherical
aberration
The world’s largest telescopes are reflectors.
The telescopes of Mauna Kea
Observatory on La Palma
From left to right, the William Herschel Telescope, Dutch Open Telescope, the Carlsberg
Meridian Telescope, the Swedish Solar Telescope, the Isaac Newton Telescope (second
from right) and the Jacobus Kapteyn Telescope (far right) at Roque de los Muchachos.
(Photo by Bob Tubbs)
European Southern Observatory (ESO) in Chile. (Copyright: R. Rekola)
3.2 Capabilities of a telescope
  The angular magnification is given by the ratio of the
focal length of the objective lens/mirror to the focal
length of the eye piece - objective lens/mirror of a longer
focal length produce bigger (in what sense?) images:
M ~ f1/f2
f1
Objective lens
f2
Eye piece
  The light gathering power of a telescope is proportional
to the area of the objective lens/mirror, which is
proportional to the square of the lens/mirror diameter bigger telescopes produce brighter images.
L
D2 R 2σT 4
2
-1
2
P = Fobs A =
π
=
π
D
(J
s
)
∝
D
4 πd 2 4
4d 2
€
Ex.1: The pupil size of the human eye is about 5mm, and its focal length is
17mm. The largest refractor ever built has a diameter of 102 cm and focal
length of 19.5 m. (a) How many times greater is the light gathering power
of this telescope compared to that of human eyes? (b) What’s the
magnification of the telescope if the focal length of its eyepiece is the same
as that of the human eye?
⎛ 102 cm ⎞2 ⎛ 1020 mm ⎞2
2
4
(a) ⎜
⎟ = ⎜
⎟ = 204 = 4.2 × 10
⎝ 5 mm ⎠
⎝ 5 mm ⎠
19.5 m 195000 mm
(b)
=
= 1.1 × 10 3
17 mm
17 mm
€
€
  The angular resolution of a telescope is limited by
diffraction: bigger telescope, more details.
Diffraction limited angular resolution:
5 λ
θ = 2.5× 10
D
θ = diffraction limited angular resolution, in arcsec
λ = wavelength of light, in meters
D = diameter of telescope objective, in meters
The angular resolution of a telescope determines how much
detail we may see in an image -- the angular resolution of human
eyes is 1 arcmin, and all planets have angular size of or less than
1 arcmin.
Ex.2: Diffraction limited angular resolution of Keck Telescopes
(D = 10m): θ
= 2.5x105 (550nm/10m) = 0.01 arcsec.
Ex.3: To have 1 arcsec angular resolution by observing at microwave
wavelength (3 cm), how big a mirror is needed?
D = 2.5
x 105 (λ/θ) = 2.5x105 (0.03 m/1) = 7500 m (!)
Aiming at large telescopes:
the larger the aperture, the brighter is the image.
the larger the aperture, the more details we can see…
Q: shall we build telescopes of larger objective focal
length to better resolve an image?
3.3 Atmosphere turbulence and light pollution
In reality, telescope images are degraded by the blurring effects of the
atmosphere and by light pollution. The angular resolution limited by the
atmosphere turbulence is called seeing. Seeing varies at different
locations. Telescopes are desirably operated at good-seeing sites (e.g.
Mauna Kea, seeing = 0.5”).
Ex.4: Big Bear Solar
Observatory build on a
mountain top (7000 feet)
in the middle of a lake to
minimize effects by smog,
clouds, and atmosphere
turbulence. The best
seeing at this site is
around 1”, i.e., one
thousandths of the Sun’s
radius.
Q: limited by seeing, shall we
operate big telescopes on
the ground?
Adaptive optics (AO) is a smart technique to compensate for
the atmosphere turbulence by deforming the flexible mirror
controlled by a very powerful computer and fast-acting
mechanical devices.
Ex.6: Applying adaptive optics to retrieve
high resolution observations of a sunspot.
Ex.5: Observing Neptune
without and(Image
withCredit:
AO. Philip Lau)
By National Optical Astronomical Observatory
Adaptive optics
(AO) uses a
deformable mirror
to correct the
distorted wave
front by
atmosphere
turbulence.
Image credit:
http://subarutelescope.org
3.4 Spectrograph
Spectroscopy is one of the most important parts of observational
astronomy. Spectral observations can tell us the temperature,
chemical composition, and motion of remote celestial objects.
A prism spectrograph
Ex.7: Spectral observations of the Sun.
Ex.8 Hα line observed in the
Sun’s atmosphere.
Hα line
Ex.9: Dopplergram showing oscillations
in the Sun’s photosphere.
3.5 Interferometry - radio telescopes
Radio telescopes make images with interfering radio signals
from many radio telescopes separated by many kilometers.
The distance between the telescopes is a baseline. The
longer the baseline, the higher the resolution. θ ~ λ → λ
D
b
The Very Large Array (VLA,
New Mexico) consists of 27
€radio telescopes.
Radio Jupiter
Credit: I. de Pater (UC Berkeley) NRAO,
AUI, NSF
Ex.10: Radio Jupiter recorded at
VLA, New Mexico. The radio
waves mapped in this false-color
image are produced by energetic
electrons trapped within Jupiter's
intense magnetic field. The radio
emitting region extends far beyond
Jupiter's cloud tops and surrounds
Jupiter. While it glows strongly at
radio wavelengths, Jupiter's
radiation belt is invisible in the
more familiar optical and infrared
views which show the Jovian cloud
tops and atmospheric features in
reflected sunlight. NB: this type of radio emission is a non-thermal emission, different from
blackbody continuum radiation or line emission.
3.6 Space telescopes
Telescopes in orbit are free of atmosphere turbulence and can
observe at wavelengths to which the Earth’s atmosphere is
opaque.
The atmosphere is transparent in three wavelength regions,
optical window, radio window, and some parts of near
infrared.
Telescopes in the space can observe dusts around stars and
galaxies in infrared, hot stars and gas, the Sun’s corona, and
planets atmosphere in ultraviolet and X-rays, and some very
energetic phenomena in γ-rays.
The Hubble Space
Telescope (HST)
launched in 1990
had a 2.4-meter
objective mirror and
was designed to
observe at
wavelengths from
115 nm (ultraviolet)
to 1µm (infrared).
HST uses a CCD to
record images. HST
has made numerous
discoveries.
The James Webb Space Telescope (JWST) to be launched soon will
have a 6.5m diameter objective mirror, and observe from 600nm to 28
µm. (http://www.jwst.nasa.gov/)
ROSAT
ASCA
X-ray telescopes
The Compton Gamma Ray
Observatory (CGRO) detect
Gamma ray and hard X-ray
bursts.
TRACE
RHESSI
Ultraviolet,
X-ray, and
Gamma ray
space
telescopes
observing the
Sun.
The entire sky at five wavelength
ranges: visible, radio, infrared
(IRAS), X-ray (ROSAT), and
gamma-ray (CGRO) showing
different structures of the Milky
Way and beyond.
Key Words
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adaptive optics
angular resolution
baseline
chromatic aberration
chemical composition
diffraction
focal length
focal plane
interferometry
magnification
objective lens
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objective mirror
optical telescope
radio telescope
reflecting telescope
(reflector)
refracting telescope
(refractor)
seeing
spectrograph
spherical aberration
Summary:
  Refracting telescopes (refractors) form images by bending light rays to
a focus point through glass lens. They have shortcomings like chromatic
aberration, glass defects, and distortion by weight.
  Reflecting telescopes (reflectors) form images by reflecting light rays to
the focus from curves mirrors, most used in modern astronomy.
  Theoretically, a telescope’s diffraction limited angular resolution
depends on the diameter of the objective and observing wavelength.
  Atmosphere turbulence and light pollution blur telescope images.
Adaptive optics can be applied to ground-based telescopes to correct the
atmospheric distortion.
  Radio telescopes use interferometry techniques to achieve high
resolution images.
  Telescopes in space are free from the Earth’s atmosphere turbulence
and are able to observe light at wavelengths - infrared, ultraviolet, X-ray,
and gamma-ray - blocked by the atmosphere.
References: FK Chap 6. & Lecture notes
Star trails above Mauna Kea
(Peter Michaud, Gemini Observatory)