# Topic 2: Telescopes and imagesTopic 2: Telescopes and images

Brief intro

The shadows of the moon are sometimes smooth or rough- this was due to mountainsàchallenged views of perfect and unchanging heavens.

Use telescopes to study electromagnetic from distant objectsàdata collected led to new discoveries

Optical telescopes use VISIBLE light

Star charts can calculate a ship’s position = navigation

Discovering what’s out there 2A

Aperture – a gap that collects radiation

Telescopes have bigger apertures than the naked eye thus they can collect more light and radiationàcan study fainter objects e.g. stars

Pulsars – Distant objects that send out radio waves that vary with an extremely regular pulse (e.gm1.3 secs apart)

Green clouds = warm gas             Red spots = gas becoming sports              Dark patches = remains of supernovae

Making images of distant objects 2B

Real image – It can be formed on the screen because the light rays actually meet after refraction

Real image ray diagram

Real image steps:

1. Make a pinhole in card
2. Light rays pass through the pinhole
• The upper and lower rays are travelling at a slight angle through the hole
• The upper ray becomes the lower ray when the light passes through the hole and vice versa.
1. The scattered light rays makes various spots of lights (points) on the screen à image formed
2. The image is inverted (b/c the light rays have gone from UP to LOW and vice versa)

The sun’s image

The sun is a star. Stars are very far away and thus they are point sources (spots of light) on the screen.

The image will get fainter if the object is further away, because fewer point sources reach the screen.

If the light rays stretch, the image also stretches à bigger image

How do lenses work? 2C

1. Light rays enter the lens
2. Light rays refract (bend) and change direction slightly
3. Principal axis does not refract
4. The light rays refract again on leaving the lens
5. Principal axis does not refract
6. All the rays converge at the focal point
7. The surface must be evenly curved for the light rays to meet at the F.P; if the surface is uneven à poor, blurry image.

Curvature

Less curvature à light rays are refracted less and at a less steep angle à  Longer F.L = Less power in the lens

More curvature à light rays are refracted more and at a steeper angle à Shorter F.L = More power in the lens

Short F.L = More power                                                Long F.L = Less power

Formula:              Power (D) = 1/F.L  e.g. 1/0.5cm = 2 dioptres of lens power

Extended sources

Extended sources (e.g. sun, moon) are v. far away thus they are point source to the naked eye.

Light rays from extended sources are all parallel because it takes a long time to reach the lens.

Parallel rays that are at an angle to the principle axis converge to one side of the principal focus.

The image will form between the two F.P’s.

Converging and diverging

Real – It can be formed on the screen because light rays converge after refraction

Virtual-It cannot be formed on screen because light rays do not meet after refraction

Convex = Converging Lens                                                          Concave = Diverging Lens

• Inverted real image is formed                                           – Small, upright virtual image is formed

Refraction of water waves

Refraction – Light changes direction when it passes at an angle from one material to another

E.g. Light travel from air to glass in a lens

Wave speed = Frequency x Wavelength

Water waves in constant depth are equally spaced. Thus, the waves don’t slow down as they travel; rather the wave speed stays the same.

Speed of wave can be affected by the medium that it is travelling in e.g. shallow/deeper

Deep = bigger W.L = faster

Shallower = shorter W.L = slower

Usually, denser medium = slower travel b/c more molecules to get past BUT because deep water has a higher wavelength, the velocity increases

Speed changes = Wavelength changes (fatter/skinnier)

BUT the frequency (height) is fixed for the waves in the shallow and deep end

At 90 degree angle

If the wave hits the dense boundary (black line) to the next medium “face on”, the wave speed will slow down but it will carry on in the same direction. It will have a shorter wavelength but same frequency of the other medium.  This means that it will take more waves to travel the same distance, thus the speed will be slower.

Not at 90 degree angle

If the wave hits the medium at an angle/boundary that isn’t 90 degrees, only one part of the wave will hit the boundary first and slow down, whilst the other part will carry on at a faster speed for a while. Because they are travelling at different speeds, the wave gets slightly bent on one side. Soon the rest of the wave follows the bending. This is a refracted wave.

Applying wave theory to lenses

1. Light ray travels through air
2. Light rays hits the surface of the glass lens and slows down b/c travelling through denser medium
3. One part of the light ray hits the CURVED, and therefore not 90 degree angled, surface and slows down first
4. As it slows, it begins to bend towards the normal
• The normal is the line at 90 degrees to the boundary
1. As the light ray is leaving the glass to the air, it bends away from the normal
2. The light ray speeds up again because air is less dense thus there are fewer particles to travel through

Enter = towards the normal                                        Leave = away from the normal

Diffracting telescopes 2D

Optical DIY telescope

2 converging lens aligned to have same principal axis and focal point in the same place can make a telescope.

Eyepiece = stronger lens + next to the eye          Objective lens =weaker lens + nearer to the object than the eye

You can focus an image by adjusting the separation between the two lenses in order to get a clearer image.

DIY process

1. Objective lens collects light from distant object
• Parallel rays enter from extended sources
1. Light rays refract and converge at the focal point to create a real image
2. Eye piece lens is stronger thus has more curvature and power.
• Acts as a magnifying glass on the real image to make a virtual image

Aperture – the light gathering area of an objective lens/mirror

• Large aperture = more light/radiation gathered from distant objects àcan see distant objects clearer
• The objective lens needs to be big for the aperture to be big.

Angular size

To the naked eye, the moon has an angular size of 0.5 degrees.

What is the angular size if the magnification is 50?                            Answer:               0.5 x 50 = 25 degrees angular size

If the angular size is bigger, the image will also be bigger.

The angle between the eyepiece rays and the principal axis is larger than the angle between the objective lens rays and the principal axis, which is smaller. Thus, an extended source will look bigger through a telescope.

Stars

Telescopes don’t make starts look bigger – they are too far away, so much so that even with a telescope, they still look like point sources.

Telescopes spread out groups of stars by magnifying the angles between them. This makes them look separate from each other. The stars have been resolved.

Possible question: Show that 4 telescopes of diameter 8m gathers as much light as one telescope of diameter 16m.

Working out:     8 x 2 = 16m          à           16m = 1600cm             à                 1600/2 = 800.

OR                          8m = 800cm        à           800 x 4 = 3200cm       à                  3200/4 = 800.

Calculating magnification:    F.L of OL / F.L of EP                    OR      Fo / Fe   OR   Power eye / Power objective

e.g.        Fo = 4.5                 Fe = 0.1                   à           Magnification = 4.5/ 0.1 = 45

e.g.        0.2 D OL                8D EP                     à           Magnification = 8 / 0.2 = 40

Analysing light 2E

Spectrometers – Measure the amount of radiation received at different frequencies = different colours

Spectrometers can be attached to telescopes to show different frequencies of light in stars

Red = Lowest frequency but higher wavelength

Blue = Highest frequency but shorter wavelength

Prisms

Visible light has a mixture of wavelengths and frequencies of coloured light

Rectangular prisms

Rectangular prisms have parallel boundaries

• Rays bend one way when entering the prism
• Bend in the same direction at the same angle when leaving
• Thus, light entering glass is parallel to light leaving the glass à white light emerges

Triangular prism

1. Boundaries aren’t parallel in triangular prism. This means that some of the light colours from the visible light hit the prism first and slow down.
• Because the boundaries aren’t parallel, different colours reach the boundary at different times.
1. This small speed difference is enough to split the light into different colours that are refracted at different angles.
• Violet has the shortest wavelength therefore it takes more waves to reach the same distance to the next boundary.
• However, it is refracted at a steeper angle.
1. Because they are now travelling at different speeds because they have different frequencies, this means that they are unable to recombine to form visible light once they leave the boundary.
• They don’t recombine when they leave the prism so their personal colour is shown = spectrum
1. This splitting of light is called dispersion

You can recombine the dispersed light into visible light by using another upside down prism.

Grating

Diffraction –Light waves bend/curve and spread in this new curved shape

Diffraction grating has a set of narrow, evenly spaced parallel slits/lines which enables light to diffract.

When white light passes through the slits, the different wavelengths of coloured light are diffracted by different amounts.

This allows many spectra to form at different angles.

Astronomers use spectra to analyse light from stars.

Telescopes also have detectors that tune into specific frequencies so you can observe only one colour of light.

Lenses or mirrors 2F

Lenses = refractorsà refracts to focuses light

Mirror = reflector à reflects to focus light + EM radiation

Coloured light has different frequencies à travel at different speeds à refract by different amounts à focal points are at different points e.g. some may be closer, some further.

Lenses

Cons of lenses

• Diameter is too big à lens will sag à cannot focus the light
• Diameter too big à more curvature à light is absorbed àobjects appear fainter
• Difficult to make glass surface uniform in composition e.g. equal surfaces
• Glass lens only focuses visible light, not ER b/c they are absorbed when passing through

Mirrors

Concave lens is used as objective lens instead of convex.

Concave lens have a parabolic curve; the mirror is inside of this curve.

Law of reflection:

Angle of incidence = angle of reflection

Parallel rays reflect on a mirror and all of them converge at the same F.P.

Pros of mirror

• Reflects all colours the same way so they all converge at the same F.P
• Mirrors weight can be supported by the back (because the back isn’t necessary) so it won’t sag
• Mirror’s surface is smooth so the image won’t be distorted
• Mirrors can focus EM

Why are telescopes so big? 2G

1. Makes clearer image
2. Bigger aperture = detects fainted objects e.g. point sources

Low resolving power in telescope à Blurred image = cannot distinguish or resolve much detail

Diffraction

When waves go through a gap they bend (diffract) and spread in this bent form, to the region behind the barrier.

Diffraction is bad b/c the waves spread to the edges of the aperture and produce a blurred image.

The amount of diffraction depends on the size of the gap relevant to the wavelength of the wave.

Narrow gap: If the gap is approximately the same size as the wavelength, the waves beyond the gap will be perfect semicircles = bad b/c à blurry image

Bigger gap: If the gap is bigger than the wavelength, the waves don’t bend as much so there is little diffraction = good b/c waves don’t reach the edges of the aperture à clearer image

So you need a bigger aperture (gap) than the wavelength, to reduce diffraction.

For optical astronomers diffractions isn’t a problem b/c the wavelength of light is v. small, so you don’t need a big aperture.

Radio waves have bigger wavelengths and the aperture is too small, so the waves curve and diffract.

Using an array of telescopes = big aperture = v. high resolving power

Windows in the atmosphere 2H

The atmosphere transmits some radiation e.g. visible light, radio waves. The others are absorbed e.g. gamma.

Stars travel steadily across space for millions of years. When starlight passes through the atmosphere, there is a twinkling (scintillation).

The atmosphere isn’t uniform; it has denser areas.

When light rays pass through these different mediums/densities they refract at an angle, which changes the direction of where the light was headed.

The atmosphere is in constant movement. The denser areas refract the light in different directions à scintillation.

Issues

• Light pollution – caused by street lamps, houses etc.

These light rays scatter and enter any telescope which means that astronomer’s are not receiving the right data about the starlight.

• Radiation – caused by electrical equipment

• Water – in the atmosphere

The light gets refracted by the water à blurry images

• Dust

Light is absorbed by dust, thus not all the starlight reaches the telescopes

• Space
1. Not 100% safe Earth based telescoped are cheaper + easier to maintain.
2. Cut off from all access There are ways to remove effects of scintillation via computers.
3. Expensive

Observatories and cooperation

Too complex + expensive for single countries to build and operate a huge telescope.

International collaboration is better b/c:

• Best people = more creative and share ideas
• Better facilities
• Share resources and costs

Remote locations

• Not windy place b/c vibrations à image blurs
• You want as little atmosphere between the observatory and telescopes.

Mountains have high elevation and the atmosphere is thinner up there, which doesn’t affect the light as much

• Dry locations with low pollution b/c water refracts light
• Avoid man made light pollution + dust
• Cloudless skies b/c clouds block telescopes from the view of the sky

Cons

Expensive

Lack of access as you will be in a remote area

Environmental – the observatory would damage the habitat

Social – Workers will be hard to maintain b/c need to feed, clothes, shelter.

Computers

Pro’s of computers

• Track objects in the sky à surveys
• Programmed to reposition itself precisely and accurately
• Operates remotely via the internet so can be accessed from whenever you are = less time consuming + less money spent on travelling
• Network of telescopes worldwide; you can observe an object continuously in the night sky b/c in some area it may be light whilst in others its dark
• Can record and process data
• Computer control is vital for space telescopes