Physics Unit 5A: Astrophysics

Physics Unit 5A: Astrophysics Siobhan Parish

Telescopes Chapter One

Lenses • A converging lens makes parallel rays converge to a focus. • The point that they focus to is the principal focus/focal point of the lens • A diverging lens makes parallel rays diverge • The point where the rays come from is the principle focus/focal point of the lens • The distance from the lens to the principal focus is the focal length of the lens • The plane on each side of the lens perpendicular to the principle axis containing the principle focus is the focal plane

Lenses Investigating the converging lens • Object at different distances beyond the principal focus. Position of the screen is adjusted until a clear image is seen. Image is real because it is formed on the screen where the light rays meet. If the object is moved nearer the lens, towards the principal focus, the screen must be moved further away. The nearer the object is the to the lens the larger the image is Lampbox

Lenses • Object nearer to the lens than the principal focus. Magnified image is formed as lens acts as a magnifying glass. Image can only be seen when you look into the screen from the other side to the object. Image is called virtual because it’s formed where the light rays appear to come from Lampbox

Lenses Ray Diagrams Focal length represented by f, object distance u. Can find the nature of the image formed by a ray diagram by drawing a to scale ray diagram • Lens is a single line where refraction takes place • Straight line through the centre of the principal lens perpendicular to the lens is the principal axis • The principal focus F, is at the distance from the lens on both sides • Object represented by an upright arrow

Lenses To form a real image the object must be beyond the principal focus- image is formed on the other side of the lens to the object F 2F F 2F Real image (diminished)

Lenses To form a virtual image the object must be between the lens and the principal focus- image is formed on the same side of the lens to the object Virtual image (magnified) F 2F F 2F

Lenses How images will appear Linear magnification = This is equal to 

Lenses The lens formula For an object at on the principal axis of focal length f, at distance u from the lens, the distance v from the image to the lens is given by: • When the sign is positive then the object/image is real and when the sign is negative then the object/image is virtual • The focal length for a converging lens is always positive • Focal length for a diverging lens is always negative

The refracting telescope • Made up of two converging lenses of different focal lengths • The lens with the longer focal length is the ‘objective’ because it faces the object • The viewer looks through the other lens, the eyepiece • Light from the object enter the viewers eye after passing through the objective and then the eyepiece • By adjusting the inner and the outer tube the distance between the two objects is adjusted until the image is in focus • If being used to view a distant object, the viewer sees an enlarged, virtual and inverted image

The refracting telescope • Objective lens focuses the light rays to form a real image of the object • The light rays cross each other after passing though the objective lens • Eyepiece gives the viewer looking through the telescope a magnified view of the real image • Magnified view if virtual because it is formed where the rays emerging from the eyepiece appear to have come from

The refracting telescope Normal adjustment is when the telescope is adjusted so the image seen by the viewer is at infinity The distance between the two lenses is the sum of their focal lengths • The real image of the distant object is formed in the focal plane of the object • The eyepiece is adjusted so its focal plane coincides with the focal plane of the objective • The light rays that form the real image leave the eyepiece parallel to one another- appear to come from a virtual image at infinity

The refracting telescope Ray diagram for a refracting telescope in normal adjustment Real image Virtual image at infinity

The refracting telescope • If a telescope is in normal adjustment and it makes a distant object appear 3 times larger its angular magnification would be 3 • If the angle subtended by the distant object to the unaided eye is 1˚ then then angle subtended by the telescope to the eye would be 3˚ • The angle subtended by the final image at infinity to the viewer = β • The angle subtended by the distant object to the unaided eye = α

The refracting telescope • h1 is the height of the real image • fo is the focal length of the objective lens • fe is the focal length of the eyepiece lens • tanα = • tanβ = • To eliminate from these equations combinethem through tanα/tanβand get the result above CALCULATOR MUST BE IN RADIANS! α Real image β Virtual image

The refracting telescope Image brightness • Stars are seen as a point object and will be seen brighter through a telescope • This is because the telescope objective is wider than the pupil of the eye so can let more light in • The light entering the eye pupil or the objective is proportional to the area in each case; the area is proportional to the square of the diameter • Diameter of the pupil is about 10mm • a diameter of 60mm would collect 36 time more light per second from a star (60/10)2

The refracting telescope • The greater the diameter of the objective of a telescope, the greater the number of stars that can be seen • Planets are magnified using a telescope, where as stars are always seen as point objects • Planets are NOT seen as brighter when viewed through a telescope because the virtual image is magnified- spread over a larger part of the field view • Therefore, the amount of light per second per unit area of the virtual image is unchanged

Reflecting telescopes • A concave mirror us used instead of a converging lens as the objective in a reflecting telescope • The concave reflecting mirror is the primary mirror because a secondary smaller mirror reflects light from the concave reflector into the eyepiece • Parallel rays are reflected and focused to a point by the mirror • If rays are parallel to the principal axis then the point where the rays are focused is the principal focus, F

Reflecting telescopes • The focal length, f, is the distance from the principal focus to the centre of the mirror f F

Reflecting telescopes The Cassegrain reflecting telescope • Secondary mirror is a convex mirror near the focal point of the primary mirror • Purpose of the convex mirror is to focus the light onto, or just behind, a small hole at the centre of the concave reflector • The light passing through the small mirror then passes through the eyepiece • Distance from the concave mirror to the point where is focuses parallel rays is increased by using a convex mirror instead of a plane mirror

Reflecting telescopes The viewer will see a virtual image at infinity • The effective focal length of the objective is increased by using a secondary convex mirror • The image of a distant object is usually brought into focus by adjusting the position of the secondary convex mirror • The primary mirror should be parabolic and not spherical to avoid sphericalaberration. This would result in the outer beams being brought to focus near the principal focus, but not at it

Reflecting telescopes Comparing refractors and reflectors • Reflecting telescopes can be much wider because high-quality concave mirrors can be manufactured much wider than a convex lens can  the wider the objective is, the greater the amount of light they can collect from a star • The high quality of a wide concave mirror compared with a wide convex lens is because:- Image distortion due to spherical aberration is reduced with a parabolic mirror- Unwanted colours in the image are reduced. Unwanted colours come from the splitting of white light. This is chromatic abberation

Reflecting telescopes Reflecting telescopes Use lenses only and no supporting frames which would block light from the object Have a wider field of view than reflectors because angular magnification is less Shorter and easier to handle than refractors with same angular magnification Greater angular magnification than refractors of same length- greater magnification of distant objects Refracting telescopes

Resolving power The angular separation of two stars is the angle between the straight lines from the Earth to each star • If the telescope just resolves the two stars then the stars can just be seen as two separate images • If the telescope is replaced with one of a narrower objective then the images would overlap too much, this is because:- The objective mirror or lens in an aperture which light from the object must pass through- diffraction of light always happens here- Instead of focusing the light to a point thediffraction would cause the image to spread out slightly- Narrower the objective; greater amount of diffraction that occurs so the the greater the spread of the image θ

Diffraction D is the diameter of the circular aperture • Diffraction at a circular aperture (gap) can be observed on a screen when a narrow beam of light passes through the circular aperture before reaching the screen • The diffraction pattern on the screen shows a central bright spot surrounded by alternate bright and dark rings • The intensity of the bright rings decreases with distance from the centre • Objective of a telescope is a circular aperture containing a convex lens of concave mirror • As the light is focused by the objective, the star would be seen as a magnified virtual image of the diffraction pattern

Diffraction REMEMBER RADIANS!! • Two stars near each other can be resolved if their central diffraction spots do not overlap significantly • When writing this numerically it is known as the Rayleigh criterion this states that: the resolution of the images of two point objects is not possible if any part of the central spot lies inside the first dark ring of the other image • This means that the angular separation of the two stars must be at lest equal to the angle of diffraction of the first dark ring • Angular separation = θ

Diffraction • Resolution or resolving power are both to describe the quality of a telescope in terms of the minimum angular separation • The Rayleigh criterion applies to the detail visible in extended images as well as to stars • Refraction due to movement of air in the atmosphere causes the image of any star seen through a telescope to be ‘smudged’. Due to this, ground based telescopes with objectives of diameter greater than about 100mm do not achieve their theoretical resolution

Diffraction • The Hubble Space Telescope has clear images because the telescope has an objective of 2.4m and is above the atmosphere • It is above the atmosphere and does not suffer from atmospheric refraction • It achieves its theoretical resolution which is about 240 times greater than a 100mm wide telescope • It detects images at wavelengths from 115nm to about 1000nm- gives infrared, visible and ultraviolet images

Telescopes and technology Charge-couple devices • The CCD is an array of light-sensitive pixels which become charged when exposed to light • When they have been exposed to the light for a certain length of time a capacitor collects the charge in sequence through a connection to an output electrode • The voltage of the output electrode is electronically read and the capacitor is discharged before the next pulse is received • The output electrode produces a stream of voltage pulses, each ones amplitude is proportional to the light energy

Telescopes and technology • Each pixel has three small rectangular metal electrodes which are separated by a thin insulating layer of silicon dioxide which is the light sensitive material underneath • The electrodes are connected to three voltage supply rails • Rectangular electrodes and the insulating layer are thin enough to allow light photons to pass through and free an individual electron • When collecting charge, the central electrode in each pixel is at 10V and the two outer ones are at 2V  this ensures the free electrons collect under the central electrode

Telescopes and technology • After the pixels have collected charge for a certain time the charge of each pixel is shifted towards the output electrodevia the neighbouring pixels. • This is achieved by altering the voltage level of each electrode in a sequence of three-step cycles • The quantum efficiency of a pixel is the % of incident photons that free an electron • About 70% of the photons liberate an electron the quantum efficiency is about 70% • Will detect much fainter images than photographic film which only has a quantum efficiency of ~4%

Telescopes and technology Advantages of a CCD • Can record a sequence of fast-changing astronomical images which can be seen by the eye but not recorded on photographic film • Its wavelength sensitivity is from less than 100nm to 1100nm is wider than that of the human eye (350-650nm). It can be used to obtain infrared images However • They need to have a larger number of pixels in a smaller area so are expensive • Cooled to low temps using liquid nitrogen

Telescopes and technology Radio telescopes • Single-dish telescopes have a large parabolic dish with an aerial at the focal point • The atmosphere transmits radio waves in the wavelength 0.001m to 10m • Waves reflect from the dish onto the aerial to produce a signal- dish is turned by motors to scan sources and compensate for the Earth’s rotation • Amplitude of the signal is a measure of the intensity of the radio waves

Telescopes and technology • The dish is usually made of a wire mesh which is lighter than metal sheets • It is just as effective in terms of reflection provided the mesh spacing is less than ~ • The dish diameter determines the collecting area and the resolving power of the telescope

Telescopes and technology Uses of radio telescopes • Locating/studying strong radio sources in the skySome galaxies are emitters of radio waves, these galaxies are usually elliptical or spherical without spiral arms. Radio galaxies are found near the centre of clusters of galaxies and their optical images often show violent events, such as the merging or collision of galaxies • Mapping the Milky WayHydrogen atoms in dust clouds emit radio waves of wavelength 21cm- emitted when the electron in a hydrogen atom flips over so its spin changed from being in the same direction as the proton’s spin to a lower energy level. Dust clouds in the spiral arm prevent us from seeing stars etc. radio waves aren’t absorbed by dust so used to map the milky way

Telescopes and technology Infrared telescopes • Large concave reflector which focuses infrared radiation onto an infrared detector at the focal point • Used to provide images of objects in space that can’t be seen using optical telescopes • A ground-based infrared telescope has to be cooled to stop infrared radiation from its own surface swamping infrared radiation from space • Water vapour in the atmosphere absorbs infrared radiation so they must be situated in a place with dry air

Telescopes and technology • Infrared telescopes on a satellite in orbit are not affected by water vapour • The telescope still needs to be cooled to a few degrees above absolute zero to be able to detect infrared radiation from weak sources

Telescopes and technology Ultraviolet telescopes • Must be carried on satellites because UV radiation is absorbed by the atmosphere • Uses mirrors to focus UV radiation to a UV detector (would be absorbed by glass) • UV radiation is emitted by atoms at high temperatures- UV telescopes are used to map hot gas clouds near stars and study glowing comets, supernova and quasars • Comparing a UV image of an object with an optical or infrared image gives useful information about hot spots in the object

Telescopes and technology X-ray and gamma-ray telescopes • Need to be carried by satellites • X-ray telescopes work by reflecting x-rays off highly-polished metal plates • Gamma ray telescopes work by detecting gamma photons as they pass through a detector containing layers of pixels triggering a signal in each pixel it passes through • Direction of the incident gamma photons can be determined from the signals • In both, diffraction is insignificant and image resolution is determined by the pixel separation

Telescopes and technology

Surveying the Stars Chapter Two

Star magnitudes • One light year is the distance light travels through space in 1 year it equals9.5 x 1015m • One light year = speed of light x time in seconds for 1 year • Light takes about 100000 years to travel across the Milky Way galaxy • Galaxies are assemblies of stars prevented from moving away from each other by their gravitational attraction • They are millions of light years away from each other • The most distant galaxies are about ten thousand million light years from each other

Star magnitudes • Can tell if a star is close because nearby stars shift against the background of more distant stars as the Earth moves • This effect is called parallax – it occurs because the line of sight to a nearby star changes every 6 months due to the diametrically opposite positions of the Earth’s orbit in this time • The Earth’s orbit around the Sun is used as a baseline in the calculation to find the distance to the nearby star • The mean distance from the centre of the Sun to the Earth is referred to as one astronomical unit, AU1.496 x 1011m

Star magnitudes • The parallax angle is defined as the angle subtended by the star to the line between the Sun and the Earth • The angle is half the angular shit of the star’s line of sight over six months • θ is always less than 10˚ • Parallax angles are measured in arc seconds, 1 arc second = • Star distances are usually expressed for convenience in terms of the parsec (pc) 1 parsec is the distance to a star that subtends an angle of 1 arc second to the line from the centre of the Earth to the centre of the Sun

Star magnitudes • For telescopes on the ground, the parallax method for measuring distances works up to about 100pc • Beyond this distance the parallax angles are too small because of atmospheric refraction • Telescopes on the satellites can measure parallax angles more accurately and so can measure distances to stars beyond 100pc 1 parsec = 3.09 x 1016m = 3.26 light years = 206265 AU

Star magnitudes • Brightness of a star in the night sky depends on the intensity of the star’s light: light energy per second per unit area received from a star at normal incidence on the surface • The intensity of sunlight at the Earth’s surface is 1400Wm-2 • Intensity of light from the nearest star is a million million times less

Star magnitudes • Scale of star brightness is defining five magnitudes as a hundredfold change in the intensity of light received from the star • Apparent magnitude and absolute magnitude is used to distinguish between light received from a star and light emitted by the star • Absolute magnitude allows a comparison between stars in terms of how much light they emit • Stars such as Sirius are ‘first magnitude’ stars and have zero, or negative, apparent magnitudes

Star magnitudes • Apparent magnitude, m, is a measure of the brightness which depends on the intensity of the light received from the star • Absolute magnitude, M, is the star’s apparent magnitude if it was at a distance of 10 parsecs from Earth • In using the inverse square law (I is proportional to 1/d2) it is assumed that radiation from the star spreads out evenly in all directions and no radiation is absorbed in space • USE BASE 10 LOGS NOT BASE e!

Classifying stars • When viewing stars through a telescope you’ll see their true colours rather than just white light • Star emits thermal radiation which includes visible light and infrared radiation • Spectrum of light emitted shows there is a continuous spread of colours which change their relative intensities as their temperature increases • Thermal radiation from a hot object at constant temperature consists of a continuous range of wavelengths • The distribution of intensity with wavelength changes as the temperature of the object is increased

Physics Unit 5A: Astrophysics