Waves

 

Waves are oscillations in space and time.  They transfer energy from one place to another without transfer of mass.

 

They have certain characteristics:

 

Wavelength º distance between two consecutive crests (or troughs).

 

 

Period º time between two consecutive crests (or troughs)

 

 

Frequency º # of crests passing per second. (frequency = 1/period)

 

 

Wave speed º The speed at which the waves energy is transferred. 

 

The speed of a wave depends only on the properties of the medium it is traveling through.  (speed = wavelength x frequency)

 

 

Amplitude º Maximum displacement of oscillation from the average position.

Light as a Wave

 

Light is a transverse wave whose amplitude is measured in electric and magnetic fields, so it is often called electromagnetic radiation.

 

This radiation comes at any size wavelength.  Visible light only covers E-M radiation that has a range of wavelengths from 400-700 nm  (1 billion nm = 1 m).  We do not see any other wavelength radiation.

 

We perceive different wavelength light as different colors.  Violet and blue light have wavelengths around 400 nm.  Red light has wavelengths around 700 nm.

 

There are many other types of EM radiation besides visible light. We are familiar with some of these types of radiation, listed here from longest wavelength (lowest frequency) to shortest wavelength (highest frequency)

 

Radio waves

Microwaves

Infra-red radiation

Visible light

[long] Red, Orange, Yellow, Green, Blue, Violet [short]

Ultra-violet radiation

X-rays

Gamma rays

Light can be separated by wavelengths in several ways.

 

A prism will separate “white” light into to the different colors that make it up.

 

A diffraction grating, which is a series of slits that are very, very close together, cause the light to be divided up into their component wavelengths as well.

 

 

 

Telescopes

 

Telescopes are the single most important tool in astronomy.

 

We receive only a very small amount of light from celestial objects.  Telescopes allow us to gather that light, focus it and produce magnified images.

 

 

Therefore understanding what telescopes do and how they work is critical to understanding astronomy.

 

 

 

 

Refraction

 

 

When light travels from one material to another, it will change speed, when it changes speed it will change direction.

 

For example, light that is incident on a piece of glass:

 

 

 

 

 

 

 

 


Or

 

 


      

 

 

 

Lenses

 

The ability to change the direction light moves allows us to focus the light and make an image of the object.

 

A carefully made lens will focus all parallel rays of light to meet at a certain point on the other side of the lens.  This point is called the focal point.

 

The focal length is the distance from the lens to the focal point.  The focal length of a lens depends only on how much it is curved.

 

A lens manipulates the light from an object and produces an image of the object at a different position.

 

Lenses can also be used to magnify a close-by object.  (Magnifying glass)

 

 

 

 

Refracting Telescope

 

Two lenses are used to construct a telescope.  The first lens gathers the light and produces an image inside the telescope.  This lens is called the objective lens.

 

The second lens is used to magnify the image (just like a magnifying glass does) produced by the first lens. 

 

The telescope is focused when the distance between the two lenses is equal to the sum of the focal lengths of the lenses.

 

Chromatic aberration is a fuzzyness of the image due to the fact that light of different wavelengths will refract at slightly different angles.  That is, blue light focuses at a different point than red light.

 

All refracting telescopes correct this by adding an additional lens of a different kind of glass to reduce or remove this aberration.  A telescope with this correction is called an achromatic lens.

Reflecting Telescope

 

A reflecting telescope uses a curved mirror as an objective, rather than a lens. 

 

 

A curved mirror focuses light just like the refracting lens does.  An eyepiece is then used to magnify the image.

 

Since the light does do not pass through the glass in a reflecting telescope, there is no chromatic aberration.

 

For this reason, all large telescopes are reflecting telescopes.

 

 

What exactly does a telescope do for us?

 

A telescope has three attributes that improve upon the human eye’s ability to detect and focus light.

 

The first of these is the most obvious:

 

Magnification º This is the ability of a telescope to increase the angular size of a faraway object.

 

The magnification of a telescope is defined to be the angular size of the object through the telescope divided by the angular size of the object without the telescope.  Using geometric optics we can show that for a telescope that has a objective with focal length fo and an eyepiece with focal length fe, that the magnification is

 

                           M = fo/fe

 

Field of view º The area of the sky you can see through a telescope.

 

Note that as magnification increases the field of view decreases.

 

Also, as magnification increases, the brightness of the image decreases.

 

Magnification is not the only reason or even the most important reason to have a telescope.

 

The second attribute is called:

 

Light-gathering abilityº  The ability of a telescope to collect light. (Produce a brighter image)

 

Light–gathering ability depends only on the area of the objective lens or mirror.

 

       Since only a very small amount of light comes from a star at any given time, it is crucial to be able to gather as much of that light as possible.

For very distant objects long exposure times can be used to gather enough light to image the object.

The last and most important attribute of a telescope is

 

Resolution º The minimum angular separation two objects can have and still be seen as two objects.  Resolution is measured as an angle.  The smaller the minimum angular separation the better the resolution.

 

Resolution allows astronomers to see the detail of the objects there are studying.  It is the clarity of the image.

 

There are a number of factors that govern the ability of a telescope to have good resolution.

 

One of these factors is the diffraction of light.  To reduce diffraction and increase resolution the diameter of the telescope must be much, much larger than the wavelength of light that you are collecting.  (For visible light telescopes this is really not the limiting factor.)

      

 

 

                    

The Earth’s atmosphere is also a big factor in limiting resolution.  Two solutions for this 1) get above the atmosphere (mountains, orbiting telescopes) and 2) adaptive optics.

 

 

Adaptive optics has only been perfected in the last several of years.  They use a mirror whose shape can be adjusted to compensate for the blurring effects of the atmosphere.  Recent pictures taken from the Keck observatory in Muana Kea, Hawaii using adaptive optics, rival the Hubble space telescope in resolution.

 

 

 

 

 

 

 

 

 

 

 

Radio Telescopes

 

We tend to think that the visible light is all the information available from a star.  This is obviously not true.  Visible light only represents a very small portion of the light that stars and other objects emit.

 

Telescopes can be made to collect any wavelength of electromagnetic radiation, not just visible light.  However, almost all earth-bound telescopes are either visible light or radio telescopes.  (Why is that?)

 

Radio telescopes work in the same way we see visible light reflecting telescopes work.

 

Because radio waves have a much larger wavelength than visible light, to get good resolution the objectives must be very large to get reasonable resolution.

 

 

 

 

Interferometery is another way to improve the resolution of radio telescopes.  The signals received from widely separated telescopes can be combined to produce higher resolution images.