Astrophysics

What is a real image?

When light rays from an object are made to pass through another point in space.

What is a virtual image?

When light rays from space appear to have come from another point in space - the light rays are NOT where the image appears to be.

Define the variables in 1/f = 1/u + 1/v

f = focal length

u = distance between object and lens

v = distance between image and lens (v is positive if image is real, and negative if virtual)

Describe the structure of a refracting telescope.

2 converging lenses.

Define Normal adjustment.

A refracting telescope uses normal adjustment - the magnified image appears to be at infinity. f₀ > f_e (where 0 means focal length of objective lens, and e means focal length of eye lens)

Give equations for Magnification.

M = θ_i/θ_o = f₀/f_e

Where i = angle subtended by image.

and O = angle subtended by object at the eye

Describe the structure of a reflecting telescope.

2 mirrors, and a converging lens

primary mirror = concave

secondary mirror = convex

Explain why the secondary mirror is needed for reflecting (cassegrain) telescopes.

The principle focus of the light rays after reflecting off of the first mirror is in front of the mirror, so a secondary mirror is placed so that the observer doesn’t block out any light. (otherwise the observer would have to look through the same direction that light is coming into the telescope)

What is the resolving power of a telescope?

How much detail you can see.

What is the Minimum Angular Resolution?

The smallest angular separation at which the instrument can distinguish 2 points.

State the relationship between the Minimum Angular Resolution and the Resolving Power.

The smaller the MAR, the greater the RP

Give on behaviour of waves that limit the resolution of a telescope.

Diffraction. (e.g a beam of light passing through a circular aperture of a telescope causes a diffraction pattern called an airy disc)

Give the requirement needed to distinguish between 2 light sources.

The centre of the airy disk (the maxima on the diffraction pattern) one on of the light sources is at least as far away as the first minima of the other source.

Explain what is meant by the Rayleigh Criterion

It identifies the minimum subtended angle between 2 objects that can be resolved. This minimum angle occurs when the first maxima of one diffraction pattern coincides with the first minima from the other object’s diffraction pattern.

What does D and θ mean in the equation for the Rayleigh Criterion

D = Diameter of objective lens/mirror

θ = MAR in radians

To see very fine details, do the objective lenses/mirrors need to be very large or small in diameter?

Very large

Explain disadvantages of refracting telescopes

Chromatic Abberations - glass refracts the different colours of light by different amounts - blurs the image

Also may suffer from Spherical Abberations if the lens is not parabolic enough

Large Magnification requires very large focal lengths, so they are very long

Large lenses increases the likelihood of defects and impurities in the glass

Weight - Telescopes are very heavy and distort under their own weight

Explain the advantages of Refracting Telescopes.

Lower Maintenance compared to reflectors

Less sensitive to temperature changes

Explain the disadvantages of Reflecting Telescopes

Spherical Abberations - if the mirror isn’t parabolic enough so light rays dont all converge at the exact same point - blurs image

Secondary mirror blocks light entry onto first mirror, so quality of image decreases

Mirrors are exposed to air - need regular maintenance

Secondary Mirror also causes some diffraction

What are CCD’s?

They are very sensitive image detectors

Explain how a CCD works

Contain a silicone chip divided into pixels

Photons hit the chip, and electrons are released

The electrons get trapped in a potential well in the CCD

The electrons alter the charge on each pixel

The image produced is identical to the electron pattern

When exposure is complete the charge is processed to create a digital image

What is quantum efficiency?

The proportion of photons incident compared to the photons that are actually detected

Compare CCD’s to the human eye.

CCD’s have a QE of 80%, whereas eyes have a QE of 1%

CCD’s can detected Infrared, Visible and UV light, whereas eyes can only detect visible light

CCD’s have a spatial resolution of 10micrometers, whereas eyes have a SR of 100micrometers (so CCD’s better for capturing the fine details)

CCD’s can be linked to a computer for capture of images and analysis

Describe the features of a radio telescope

Parabolic dish that works in the same way as the objective mirror of a reflecting telescope.

Antenna is used as a detector at the focal point instead of an eye/camera

Explain a downside to Radio Telescopes.

For a radio telescope to have the same resolving power as an optical telescope, the dish would need to be a million times bigger.

Explain how they get over the downside of radio telescopes having such a low resolving power.

They link lots of telescopes together - and combining them to form a single image (equivalent to having one big dish)

Give some advantages of Radio Telescopes

Dish does not have to be as smooth as a mirror, as to avoid spherical aberrations it only has to have a precision of λ/20

It has a greater collecting power, as the dishes are so big, so they produce brighter images

Where can we station Optical and Radio telescopes and why?

On the earth, as as the atmosphere is transparent to these wavelengths

Where must IR telescopes be positioned?

At high-altitudes in dry places - as water vapour absorbs the IR

Where are UV and X-ray telescopes positioned, and why?

High altitude weather balloons or aeroplanes, absorbed very high up in the atmosphere - but ideally we want the telescopes above the atmosphere - launch into orbit in space.

Give 2 similarities between IR/UV telescopes and Optical Reflecting telescopes.

They both use a parabolic mirror

They both use CCD’s

Give an advantage that IR telescopes have (manufacturing wise) over Optical Reflecting telescopes

IR has a longer wavelength than light, so it is less affected by imperfections in the mirror, and don’t need to be as perfectly shaped as optical telescopes

Give a disadvantage of UV telescopes (manufacturing wise) compared to optical telescopes.

They have shorter wavelengths, so need to be more precisely made.

Give another disadvantage of IR telescopes.

They produce their own IR radiation due to their temperature, so they need to be cooled using liquid helium or fridge units

Why are X-ray telescopes constructed differently to other telescopes?

X-ray radiation doesn’t usually reflect, it either gets absorbed or passes straight through it. They do reflect if they GRAZE a mirrors surface

What is the name of the telescope used to capture X-rays and how does it work?

A Grazing Telescope. A series of nested mirrors gradually focus the X-rays enough to a detector. They can be detected using a modified Geiger counter or a fine wire mesh.

X-rays have a much smaller collecting power than other telescopes

What 2 factors is the resolving power of a telescope dependent on?

The Rayleigh Criterion

The quality of the detector (i.e CCD)

What is the Collecting Power proportional to?

The Diameter² (The area)

A bigger dish collects more energy from an object in a given time, giving a more intense image and allowing the telescope to observe fainter objects

What is a Star’s luminosity?

The total energy emitted per second (where the energy is in the for of EM radiation)

Give an equation for the Intensity of a star

I = L/4πd² (intensity it the brightness)

What 2 factors does brightness depend on?

Luminosity
Distance from us

What is the Hipparchus scale?

a scale that gives us a value of apparent magnitude, going from 1 (brightest stars) to 6 (dimmest stars)

What is the scale factor between magnitude 1 stars and magnitude 2 stars?

2.51x

Give an equation for the brightness ratio between 2 stars.

I_A/I_B = 2.51^mB-mA

Where mB and mA are the apparent magnitudes

If the angle of parallax to a star is 1arcsecond (1/3600⁰) then what distance is the star from the earth?

1 parsec

What is the absolute magnitude (M) of a star?

It is what the apparent magnitude WOULD be, if the star was 10pc away from earth.

What is different between m (apparent) and M (absolute)?

M does not depend on distance, as all stars are given a standardised distance of 10pc.

Give an equation linking m and M, and state what makes this equation special.

m - M = 5log(d/10)

d is distance measured in parsecs (and 10 = 10pc)

What is 1 AU

The mean distance between the earth and the sun

What is a lightyear?

The distance that light/EM waves travel in one year.

What is Stefan’s law?

P = σAT⁴

Why are exoplanets hard to find?

They orbit stars that are much brighter than themselves - light from star drowns light from planet
They are too small to distinguish from their stars

Name 2 methods used for finding exoplanets.

Radial Velocity Method
Transit Method

Describe the radial velocity method for finding exoplanets.

PERIODIC DOPPLER SHIFT IN LIGHT RECEIVED FROM A STAR - An exoplanet orbiting a star has a small effect on the stars orbit - causes variations in the stars orbit (because star and planet are actually orbiting a centre of mass between them - closer to the star). This causes tiny red and blue shifts in the stars emission - suggests existence of exoplanets.

Give problems with the radial velocity method.

The movement needs to be aligned with the observers line of sight

Describe the transit method for discovering exoplanets.

Measures the change in apparent magnitude as an exoplanet travels in front of a star - when planet goes in front of star, apparent magnitude drops, helps us calculate the radius of the planet

Give problems with the transit method for stars.

The chance of the planet being perfectly lined up so it crosses the line of sight between the star and earth is extremely low.