#### Transcript angular size

```4.1 EM Spectrum
Wavelength: distance between two
successive crests or troughs.
Light: is a wave of wavelength
ranging between 400 nm (violet) to
660 nm (red)
White light: consists of the rainbow colors
(red – orange – yellow – green – blue –
indigo – violet)
Electromagnetic Spectrum
Electromagnetic Spectrum
Why do we see the Sun looks
reddish at sunrise and sunset?
• The red color has larger wavelength
(longer steps).
Why do we see the sky looks
blue?
• Blue light has smaller wavelength (smaller
steps).
The relation between colors and
temperatures
• Energy is directly proportional to
frequency.
• Energy is inversely proportional to
wavelength.
• Blue is more energetic than red.
• The hotter the star, the bluer the light.
• The cooler the star, the redder the light.
Atmospheric Window
Atmospheric Window
• The atmosphere is transparent at visible
• The atmosphere is opaque at other parts
of the spectrum.
4.2 What a telescope is?
Resolution & Angular Size
Astronomers use angles to denote the positions and apparent
sizes of objects in the sky.
Angular Measure
• Basic unit of angular measure is
degree º
the
– Full circle measures 360º
– Right angle measures 90º
• Angular distance is the number of degrees
across the sky between two points.
• Angular diameter or angular size is the
number of degrees from one side of an
object to the other side.
The angular size of the Moon is 0.5º
(1/2º )
The angular size of the Sun is also 0.5º
(1/2º )
Big Dipper
(Ursa Major)
Try this: What is the angular size of this
sphere in degrees as you see it? (Answers
will vary from front to back of room)
Angular Measure for Small Angles
1º = 60 arcminutes = 60'
1' = 60 arcseconds = 60''
So 1º = 60x60 = 3,600 arcseconds =
3,600''
Test question: What is the
angular size of the Moon ( 0.5°)
expressed in arcseconds?
Telescopes
• Telescopes: might detect gamma rays,
Radio waves, or visible light (Optical
telescopes).
• Purpose of telescopes: to gather light in
order to make fainter objects detectable.
• Magnification is useful for observing Sun
and other planets.
• Stars are so far, they appear as points of
light.
Limitations of the human eye
•
•
•
•
Visible light only.
Small aperture (5 to 8 mm).
Storage & recording.
Resolution: the ability to distinguish finer
details of an image (to distinguish between
Resolution
m (arc sec) 
 ( A)
500 D(cm)
 1 arc min (Human eye)
d  m L
Eye
d = linear size of object
theta = angular size of object (in radians)
L = distance to the object
m
L
d
Example
 m  1 arc min  2.9 10 rad
4
• Dime = 2 cm = 2x10-2 m
• Find L?
• Airplane d=30 m
• L = ??
d  m L
m
L
d
Resolution of a telescope
• Is inversely proportional to the diameter of the
primary mirror or lens.
• Resolution is limited by the turbulence of
Earth’s atmosphere to about ½ arc sec.
• Increasing the size of a telescope above a
certain limit, no longer improves its resolution.
4.3 Lenses and Telescopes
• Refractor: is a telescope in which light is
collected and focused by a lens.
• Refraction: bending of light when it moves
from on substance (like air) to another (like
water).
• Objective lens: bends the light at the focus
(a focal length behind).
• Eyepiece: is used to examine and magnify
the image focused by the objective lens.
• Field of view: an image of an area of the
sky.
Chromatic Aberration: not all colors
focused at the same point.
Spherical Aberration: deviation from
perfect focusing
Opaqueness & Sagging
• Some limitations to the use of large
refractors:
– Opaqueness of the glass.
– Sagging of the lens because of gravity.
4.4 Reflecting telescope
Newtonian
Prime
focus
Cassegrain
•
•
•
•
Blocking some of incoming light.
Need to look at the top of the telescope
Needs to be cleaned often.
Both suffer from spherical aberration.
•
•
•
•
Can be made larger than refractors.
Can be supported. (No sagging problem)
Different colors focus at the same point.
Can be used for ultraviolet detection, since UV
does not pass through glass.
4.5 Light Gathering Power
• The amount of light collected by a
telescope mirror is proportional to the
area of the mirror πr2 = πd2/4
4.5a Conditions for good
observation
• Seeing: The steadiness of Earth’s
atmosphere.
– Twinkling of stars.
• Transparency: How clear the sky is.
• Light pollution:
– Why do we see more stars in the desert than
in a city.
(Mauna Kea) Hawaii
4205 m above sea level
What is special about Mauna Kea?
•The atmosphere above the volcano is extremely dry, which is
important for submillimeter and infrared astronomy because
water vapor absorbs radiation in most of this region of
the electromagnetic spectrum.
•The summit is above the inversion layer that separates lower
maritime air from upper atmospheric air, keeping most cloud
cover below the summit and ensuring the air on the summit is
dry, and free of atmospheric pollution.
•The summit atmosphere is exceptionally stable; the lack
of turbulence creates some of the world's best astronomical
seeing.
•The very dark skies resulting from Mauna Kea's distance from
city lights are preserved by legislation that minimizes light
pollution from the surrounding area.
4.5b Magnification
focal length of objective lens
Magnificat ion 
focal length of eyepiece
As the magnification increases, the field of view decreases
Example
(magnification)
focal length of objective lens
Magnificat ion 
focal length of eyepiece
A telescope of 1-meter focal length. Calculate its
magnification if the eyepiece has a focal length of 40 mm.
Example
(collecting power)
Compare the collecting power of the 10-meter telescope with
that of the 5-meter telescope.
4.6 Spectroscopy
• Break up light into a spectrum
using:
– Prism
– Diffraction grating.
• Benefits:
– Identify chemical constituents
of star’s atmosphere.
– Determine Temperature of
star’s surface.
– Find the density of the radiating
matter.
4.7 Emission Lines
• No two elements emit the same spectrum.
• Produced using a tube having low gas
pressure subjected to electric discharge.
• He was discovered using this technique.
• Elements other than those present on
Earth have never been detected.
Absorption Lines
• The gas subtracts
energy from the
continuous spectrum
passing through it.
Hydrogen
Helium
Sodium
Iron
Definitions
• Spectrum: A display of electromagnetic
frequency.
• Spectroscope: the device used to
analyze spectrum (the spectrum making
device).
• Spectrograph: if the spectrum is not seen
by eye but with a photographic plate.
4.8 Doppler Effect
• Determine how fast an object is moving
toward or away from us, but not the
tangential speed.

0
•
•
•
•
v

c
v = speed of the emitting body.
c = speed of light in vacuum.
Δλ = the change in wavelength.
λ0 = the original (rest) wavelength.
Approaching Object
•  shorter
 is  v e
– Spectral line shifts toward the blue (Blue shifted).
Receding Object
•  Longer
 is  v e
– Spectral line shifts toward the red (Red shifted).
Example
• If a star is moving away from us with a
speed of 6000 km/s then the percentage
shift in the wavelength is:
a) 2 %
b) 2 %
c) 5 %

v

d) 4 %
0
c
e) 4 %
Example
• A red light (λ=6500 A) received from a star
is observed to have a wavelength that is
130 A shorter than normal.
• Determine the radial speed of the star.
• Is it approaching or receding?
4.9 Observing at Short Wavelength
• Ozone Layer consists of O3 is located 20 to
40 km above Earth’s surface.
• Ozone prevents all radiation of wavelength
less than 3000 A from penetrating.
• Observatories in rockets for short periods or
in orbits.
• Photographic methods can be used, since
ultraviolet and x-rays have enough energy to
interact with silver grains on films.
4.10 Observing at Long Wavelength
•
•
•
•
Low energy.
Does not affect the photographic films.
Needs special devices (electronic).
Infrared: water vapor blocks them.
– Balloons carry detectors of infrared.
• Radio Waves: Karl Jansky 1931.
– Signal received 4 min earlier every day.
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