Astrophysics 13.1.1 - 13.1.5 (telescopes)

How to label a lens diagram

Non-axial rays

• The focal length doesn’t change even if parallel rays enter the lens at different angles

• They all converge on what is known as the focal plane

How to draw an accurate ray diagram

1. Draw a axial ray from the top of the object which then is refracted and passes through the focus point

2. Draw one ray from the top of the object through the centre of the lens

3. Draw a third ray which passes through the focus on the left side and leaves the lens as axial ray

4. Draw in the image formed

Ray diagram for an object beyond 2f

Object position - More than 2f away

Image position - Between f and 2f

Image orientation - Inverted

Magnified or dimished - Diminished

Application - Camera

Real image

Ray diagram for an object at 2f

Object position - At 2f

Image position - At 2f

Image orientation - Inverted

Magnified or dimished - Same size

Application - Inverter

Real image

Ray diagram for an object between 2f and f

Object position - Between f and 2f

Image position - Beyond 2f

Image orientation - Inverted

Magnified or dimished - Magnified

Application - Projector

Real image

Ray diagram for an object closer than f

Object position - Closer than f

Image position - Same size as object

Image orientation - Upright

Magnified or dimished - Magnified

Application - Magnifying glass

Virtual image

Convex Lenses

Converging lenses

Concave Lenses

Diverging lenses

Power of a lens

Lens equation

How refracting telescopes work

• Refracting telescopes use two convex lenses to form a magnified image

• The one closes to the eye is the eyepiece lens

• M = f0/fe (f0 = focal length of objective lens and fe = focal length of eye lens)

• Total length of the telescope is the sum of the two focal lengths

How to draw a ray diagram for three non-axial rays passing through a refracting telescope

1. Draw a non-axial ray through the centre of the objective lens axis to the eyepiece lens axis

2. Draw two parallel rays either side

3. These should meet at the focus and then stop on the eye lens axis

4. Draw a construction line (which must be drawn) that starts from where the rays cross over and passes through the centre of the eyepiece lens

5. The three rays emerge parallel to this line

Two ways to calculate Magnification

• M = f0/fe (f0 = focal length of the objective lens (Objective lens to focal point | fe = focal length of eye lens (Focal point to eye) )

• M = Angle subtended by image/Angle subtended by object

How reflecting telescopes work

• Refracting telescopes use a parabolic mirror to focus incoming light into a point (rather than a lens using refraction)

• A secondary mirror is placed before the focal point to reflect the rays back through a gap in the mirror

• Rays cross over then pass into the lens

• The rays emerge parallel

• This arrangement is known as a Cassegrain telescope

What’s a CCD

• Stands for charge coupled device

• They’re used to take digital images

• They are found in most cameras

CCD’s physical characteristics

• CCD’s consist of a series of silicon picture elements (pixels)

• These pixels are very small

• Not to be confused with the pixels on a screen that change colour

• Beneath each one is a potential well which can trap electrons

• Above each one is a filter to only allow certain colour photons through

How CCD’s work

Step 1:

• The filter allows only certain wavelengths (Colours) of photons to hit the pixels

Step 2:

• The photons will cause electrons in the pixels to be released into the potential wells

• The amount of electrons is released is proportional to the intensity of the light incident (number of photons)

Step 3:

• The charge is then collected from each potential well

• The amount of charge in the potential well and the colour of filter above the tells the computer what colour and what brightness needs to be displayed

CCD’s advantages over eye and photographic film

Adv:

• Quantum efficiency: -(num of photons detected/num of photons incident x 100) -Tells us how many of the photons that hit a detector are actually detected. -A CCD detects about 80%, Photographic film is 4% and eye is 1%

• Saturation: -CCD’s don’t get saturated like how photographic film does

• CCD’s can detect a wider spectrum of light vs the eye (Infrared, visible and UV)

• CCD’s capture more fine detail: -The minimum resolvable distance (spatial resolution) of the eye is around 100μm vs CCD at 10μm

• CCD’s can have long exposures to capture very faint images

Advantages and disadvantages of refracting telescopes

Adv:

• No secondary mirror blocking light (optical advantage)

Disadv:

• Chromatic aberration

• Impurities in glass

• Lens distortion

• Length of telescope

Advantages and disadvantages of reflecting telescopes

Adv:

• Cheaper to make large

• Better support structure

• Less chromatic aberration (optical advantage)

• Better collecting and resolving power (optical advantage)

Disadv:

• Spherical aberration

• Sceondary mirror blocks light

Chromatic aberration (Disadvantages of refracting telescopes)

• When light refracts through glass by different amounts depending on the wavelength of the light - so colour focuses in different places after passing through a lens

• Shorter wavelengths like blue focus to close to the lens whilst long wavelengths like red focus too far way

• In an image this causes a colour ‘bleeding’ effect at the edges

• Both types of telescope use a lens but it has a bigger effect on the larger lens in the refracting telescope

Impurities (Disadvantages of refracting telescopes)

Any bubbles or impurities in the glass absorb and scatter light so very faint objects can’t be seen

Lens distortion (Disadvantages of refracting telescopes)

Large lens are heavy and can only be supported at the edge so the shape can become distorted

Length of telescope (Disadvantages of refracting telescopes)

For large magnification long focal lengths are needed so telescopes are very long requiring big expensive buildings

Cost (Advantages of reflecting telescopes)

Large mirrors of good quality are much cheaper than large lenses

Support structure (Advantages of reflecting telescopes)

Lens can only be supported around the edge to prevent blocking light, but as not light passes through the mirror they can be supported from the back, making them less likely to distorts

Collecting power (Advantages of reflecting telescopes)

The larger the telescope the more light you collect and the dimmer the objects you can see, reflecting telescopes are easier to make larger

Better resolving power (Advantages of reflecting telescopes)

Spherical aberration (Disadvantages of reflecting telescopes)

• Occurs when the shape of the mirror isn’t a perfect parabola

• Outer rays focus too close

• Inner rays focus too far away

• The Hubble space telescope suffered from this

• It causes images to be blurry

Second mirror (Disadvantages of reflecting telescopes)

The secondary mirror can also block and diffract some of the incoming light - leading to a decrease in image clarity

Can lenses suffer from spherical aberration?

• Yes as the same effect happens

• Outer rays focus too close

• Inner rays focus too far away

• This leads to a blurry image

Diffraction of light through a circular opening

• When light passes through a circular opening (Like the opening of a refracting/reflecting telescope) then the light diffracts

• This creates a circular diffraction pattern which consists of bright rings (maxima) and dark rights (minima)

• Central maxima is known as an airy disc

Rayleigh Criterion

• When two light sources can be distinguished if the centre of the airy disc from one source is at least as far away as the first minimum of the other source

• This allows us to decide whether two stars are resolved or not

Resolving power

• The smallest angle between two stars where they can be seen as 2 distinct stars (resolved)

• Smaller angle = More powerful telescope

• Smaller the wavelength the better

• The larger the diameter the better

Arc seconds

Structure of telescopes

• Nearly all types of telescopes use a parabolic dish to focus EM radiation onto a point

• Visible, UV and infrared telescopes place a CCD at this point

• Radio telescopes use a combination of amplifiers to boost weak signals and a tuner to focus on specific frequencies

• X-rays are absorbed by a dish so a different structure is needed -They use a series of ‘grazing’ mirrors to focus the X-rays -This makes X-ray telescopes very long

• A Geiger counter, CCD or charged metal mesh is used as a detector

Perfection of telescopes

• How perfect the dish of a telescope needs to be depends on the wavelength being collected

• An imperfections cannot be greater than 1/20th of the wavelength

• Imperfections count as bumps/holes in the dish

• UV telescopes have to be the most perfect making them very expensive

• Radio can be the least perfect which makes them cheaper and also much larger -Their dishes are often not solid but made of a mesh

Resolving power of a telescope

• Higher resolving power means a small minimum angle when two stars can be resolved

• Resolving power is directly proportional to wavelength. Also directly proportional to diameter.

• UV and x-rays have much higher resolving power whilst Radio’s the worst

Collecting power of a telescope

• Collecting power is linked to the area of the telescope (Collecting power is directly proportional to the diameter²)

• Larger telescope area can collect more photon

• This allows you to see the dimmest stars (as few of their photons reach us)

• Radio telescopes therefore have the best collecting power

• UV and X-ray telescopes tend to be small as they are expensive to make, so they have the worst collecting power

Location of a telescope

• The atmosphere blocks some wavelengths more than others -Most infrared,UV and X-ray’s are blocked so their telescopes are put into space

• However infrared telescopes can be put on top of high mountains or in airplanes to get above the atmosphere

• Visible and radio passes through the atmosphere so these can be on the ground

• However some visible light is blocked so these are more effective in space

Additional points for non-optical telescopes

• As infrared radiation is heat, the infrared telescopes have to cool themselves

• Supply of coolant will only last a few years

• Images produced by a telescope are only as good as the detector (How many pixels are on the CCD)

Parallax method

Parsec

1 Parsec is the distance when 1Au subtends an angle of 1 arc second

What’s the shortcut to find the distance when an angle is subtended?

Only use it to verify answer

Lightyear

The distance that light travels in a year