astrophysics

purpose of convex/converging lens

focuses incident light

purpose of concave/diverging lens

spreads out incident light

define principal axis

the line passing through the centre of the lens at 90 degrees to its surface

principal focus in converging lens

the point where incident beams passing parallel to the principal axis will converge

principal focus in a diverging lens

the point from which the light rays appear to come from

same distance either side of the lens

define focal length

the distance between the centre of a lens and the principal focus

relationship between focal length and strength of lens

shorter focal length, stronger lens

define real image

image formed when light rays cross after refraction

can be formed on a screen

define virtual image

formed on the same side of the lens

light rays do not cross, so virtual image cannot be formed on a screen

lens formula

1/u + 1/v = 1/f = power

u - distance of object from centre of lens

v - distance of image from centre of lens

f - focal length of lens

what does power of a lens measure

how closely a lens can focus a beam that is parallel to the principal axis

relationship between focal length and power of lens

shorter focal length, more powerful the lens

what is power of lens measured in

dioptres

formula for magnifying power/angular magnification (M) of a telescope

M = angle subtended by the image at the eye / angle subtended by the object at the unaided eye

larger angle over smaller angle

angular magnification when both angles are less than 10 degrees

M = large angle / small angle

= focal length of objective lens / focal length of eyepiece

define collecting power

a measure of the ability of a lens or mirror to collect incident EM radiation

describe collecting power

increases with size of objective lens/mirror

directly proportional to area of objective lens

greater collecting power = brighter image produced by telescope

define resolving power

the ability of a telescope to produce separate images of close-together objects

criteria for an image to be resolved

the angle between the straight lines from earth to each object must be at least the minimum angular resolution (theta = lambda / D)

define rayleigh criterion

2 objects wont be resolved if any part of the central maximum of either of the images falls within the first minimum diffraction ring of the other

define charge coupled device (CCD)

an array of light-sensitive pixels, which become charged when they are exposed to light by the photoelectric effect

define luminosity and units

rate of light energy released/power output of a star / W

define intensity

the power received from a star per unit area

the effective brightness of an object (but varies depending on the observer as brightness is subjective)

what does intensity of star follow and what does this mean

inverse square law

it is inversely proportional to the square of the distance from the star

define apparent magnitude

how bright the object appears in the sky

depend on a star’s luminosity and distance from the earth

define + describe the Hipparcos scale

classifies astronomical objects by their apparent magnitudes

brightest have apparent magnitude 1

faintest visible have apparent magnitude 6

how does hipparcos scale work

its logarithmic

as magnitude changes by 1, intensity changes with ratio 2.51

e.g. magnitude 5 star is 2.51 times brighter than a magnitude 6 star

difference between apparent and absolute magnitude

apparent magnitude of object depends on its distance from the earth

absolute magnitude doesnt

define absolute magnitude of an object

what apparent magnitude would be if it were placed 10 parsecs away from the earth

define parallax

the apparent change of position of a nearer star in comparison to distant stars in the background

how is parallax measured

using the angle of parallax

greater the angle of parallax - closer the star is to earth

define astronomical unit (AU)

the average distance between the centre of the earth and the centre of the sun

define a parsec

the distance at which 1 AU subtends an angle of 1 arcsecond

angle of parallax is 1 arcsecond

how to find distance from earth to star

use trigonometry

tantheta = opp/adj

tantheta = r/d

d = r/theta as theta is small

d = 1/theta for d in parsecs and theta in arcseconds

define a black body radiator

a perfect emitter and absorber of all possible wavelengths of radiation

stars can be approximated as black bodies

define stefan’s law

the power output of a black body radiator is directly proportional to its surface area and its (absolute temperature)^4

what can stefans law be used for

comparing the power output, temperature and size of stars

define wien’s displacement law

the peak wavelength of emitted radiation is inversely proportional to the absolute temperature (T) of the object

define peak wavelength

the wavelength of light released at maximum intensity

what does wien’s law show

that the peak wavelength of a black body decreases as it gets hotter

meaning the frequency increases so the energy of the wave increases

what can wiens’s law be used for

to estimate the temperature of black-body sources

relationship between intensity of star, power output by star and distance from star

and why

I = P/4pid^2

cuz assumed that light is emitted equally in all directions from a point so spread out in shape of sphere

ccd vs human eye quantum efficiency

ccd about 80%

human eye 4-5%

ccd vs human eye spectral range

ccd infrared, uv, visible

human only visible light

ccd vs human eye pixel resolution

ccd varies but abt 50 megapixels

human about 500 megapixels

ccd vs human eye spatial resolution

ccd 10 micrometers

human 100 micrometers

ccd vs human eye convenience

ccd needs to be set up but images produced are digital

human eye simpler to use as there is no need for extra equipment

how are stars classified into spectral classes

based on the strength of absorption lines

how do absorption lines work and why

theyre dependent on the temperature of the star

because the energy of the particles which make up the star is dependent on its temperature

define hydrogen balmer lines

absorption lines found in the spectra of O, B and A type stars

what are hydrogen balmer lines caused by

the excitation of hydrogen atoms from the n=2 state to higher/lower energy levels

hydrogen balmer lines if temp of star too high

majority of hydrogen atoms excited to higher levels than n = 2 or electrons ionised

no hydrogen balmer lines

hydrogen balmer lines if temp of star too low

hydrogen atoms are unlikely to become excited (or may not be present at all)

hydrogen balmer lines will not be present

spectral class O

blue

25000-50000K

He +, He, H

weak

intensity of hydrogen balmer lines depends on

temperature

things to know about spectral classes

colour

temperature range in kelvin

prominent absorption lines

prominence of hydrogen balmer lines

spectral class B

blue

11000-25000K

He, H

slightly stronger than O

spectral class A

blue/white

7500-11000K

H, ionised metals

strongest

spectral class F

white

6000-7500K

ionised metals

weak

spectral class G

yellow/white

5000-6000K

ionised metals and neutral metals

none

spectral class K

orange

3500-5000

neutral metals

none

spectral class M

red

<3500K

neutral atoms, titanium oxide

none

describe temperature scale on HR diagram

logarithmic

halves at every interval

sun star type spectral class and abs mag

main sequence

G

4.83

define a binary system

one where two stars orbit a common mass

define type I supernova

a star accumulates matter from its companion star in a binary system and explodes after reaching a critical mass

define type II supernova

the death of a high-mass star after it runs out of fuel

define type 1a supernova

a type I supernova with a white dwarf

shared features of all types of supernovae

occur at same critical mass

meaning very similar peak absolute magnitude (about -19.3)

produce very consistent light curves

allowing astronomers to use them as standard candles

what are standard candles used for

calculating distances to far-off galaxies

what does hubbles law do

shows the universe is expanding

and estimates age of universe

why scientists believe that supermassive black holes are at the centre of every galaxy

stars and gas near the centre of galaxies appear to be orbiting very quickly

must be supermassive object at centre with very strong gravitational field attracting them

define the doppler effect

the compression or spreading out of waves that are emitted or reflected by a moving source

as source is moving, wavelengths in front are compressed and wavelengths behind are spread out

example of doppler effect

can be heard in the sound of a car moving past you

what does doppler effect cause

causes the line spectra of distant objects to be shifted either

towards the blue end of the visible spectrum when they move towards the earth (blue-shift)

or towards the red end of the spectrum when they move away from the earth (red-shift)

what is red-shift used for

as evidence for the expanding universe, as distant objects are red-shifted

the more distant the object, the greater its red-shift

why is the wavelength ratio negative for the red shift formula

because wavelength is inversely proportional to frequency

z value for red shift pos and neg

positive for red-shift, negative for blue-shift

what can the doppler effect be used for

identifying binary star systems

define spectroscopic binaries

binary star systems where stars are too close to be resolved by a telescope

so only way to identify them is using the doppler shifts of each star

define eclipsing binaries

when the plane of the orbit of the stars is in line of sight from earth to the system

stars cross in front of each other as they orbit

how can eclipsing binaries be identified

from their characteristic light curves

describe quasars

objects which have very large red shifts

suggesting they are very far away

however they are also extremely bright

how can you show that the power output of a quasar must be around that of an entire galaxy

using the inverse square law

define hubbles law

a galaxy’s recessional velocity is directly proportional to its distance from the earth

universe is expanding from a common starting point

what does big bang theory suggest

universe began with an explosion from one point - a singularity that was infinitely small and infinitely hot

define cosmological microwave background radiation and its purpose

microwave radiation that has been detected from all directions in space

provides evidence for big bang

what caused CMBR

big bang happened

there was high-energy radiation everywhere

as universe expanded and cooled, this radiation would have lost energy and been red-shifted

remains of this is CMBR

define a quasar

an active galactic nucleus - a supermassive black hole surrounded by a disc of matter

as it falls into black hole, causes jets of radiation to be emitted from the poles

defining characteristics of quasars

extremely large optical red-shifts

very powerful light output

size not much bigger than a star

how to estimate power output of quasars

using inverse square law for intensity

by using amount of doppler shift experienced by quasar to find their distance from earth

what are quasars thought to be

some of the most distant measurable objects

what does inverse square law show about quasars

they are extremely powerful

they can have the same energy output as several galaxies

define exoplanets

planets that are not within our solar system

they orbit other stars

why can exoplanets be difficult to detect directly

they tend to be obscured by the light of their host stars

two methods of detecting exoplanets

radial velocity method

transit method

power of lens in converging and diverging lens

converging - positive

diverging - negative

power of lens formula

= 1/u + 1/v = 1/f

what are refracting telescopes made of

two converging lenses

objective lens and eyepiece lens