Astrophysics

What is the unit for power of a lens?

Dioptres (D)

What is the assumption made when using the inverse square law?

No light is absorbed or scattered between the source and the observer and that the source can be treated as a point.

What were quasars first thought to be?

Stars in our galaxy

Outline the circumstances during which a gamma ray burst will be emitted by a star

When a supergiant is collapsing

To form a neutron star or black hole.

(the important aspects of the GRB are that the star must be a supergiant that is collapsing into a neutron star or black hole)

3 properties of a reflecting telescope in normal adjustment?

The final image formed is at infinity (therefore the eye is behaving in the same way as it is when viewing the object unaided - ‘rays leaving eyepiece/entering eye are parallel’)

The principle focus of the objective lens is in the same position of the principle focus of the eye lens

distance between lenses is fo + fe - where fo and fe are defined

Explain two reasons how CCD’s improve the ability of astronomers to observe dim stars.

Difficulties in the direct detection of exoplanets.

Exoplanet may be orbiting star much brighter than itself, so hard to see it.

Usually too close to their stars to be resolved with most telescopes

Why can the transit method only be used to confirm exoplanets?

• The dip if the planet’s orbit is aligned such that it crosses our line of sight from Earth.

• If the planet’s orbit is tilted even slightly, no transit will be seen, even though the planet is still there.

Why does the radial velocity method sometimes fail to detect exoplanets?

• The radial velocity method for detecting exoplanets only works if the star wobbles toward and away from us.

• If the planet makes the star wobble side to side, we won’t see a Doppler shift.

State what is meant by a supernova (its defining property)

Objects which exhibit a rapid and enormous increase in absolute magnitude.

What are the defining properties of a neutron star?

Extremely dense (4×10^17kgm^-3)

Made up of neutrons

(Ignore descriptions of Neutron star surface Ignore refs to spinning or producing radio waves)

(A neutron star is believed to have the density of nuclear matter and be relatively small (about 12 km in diameter))

Some scientists are concerned about the consequences for the Earth of a supernova occurring in a nearby part of the galaxy. Explain the cause of this concern. (2 marks)

Collapsing star can produce gamma ray bursts with energy similar to total output of Sun

Highly collimated – if in direction of Earth, could cause mass extinction event

State one reason why it is difficult to make a direct observation of this planet.

Star much brighter than reflected light from planet

Planet very small and distant – subtends very small angle compared to resolution of telescopes

Why is the use of stellar parsec limited on both earth and in orbit? What should be used for distances greater than 300 pc?

• The parallax angle becomes too small to measure accurately at large distances (1)

• Even in orbit, telescopes have a limit to angular resolution (e.g. microarcseconds) (1)

• For distances greater than 300 pc, standard candles such as Cepheid variables should be used (1)

What is a subjective scale of measurement?

BRIGHTNESS!

What is the density of a neutron star?

4×10^17 (The density of nuclear matter)

What is the definition of collecting power?

The rate at which useful energy is received by a telescope (its directly proportional to the dish diameter²

Benefits of larger aperture diameter in terms of collecting power and resolving power?

Greater collecting power - brighter image

Better resolving power - clearer image

What is the difference between luminosity and intensity?

• Luminosity is the total power output per second of a source (like a star), measured in watts (W).

• Intensity is the power received per unit area, given by I=PAI = \frac{P}{A}I=AP​, measured in W/m².

What is equation for lens power?

P = 1/f (where f is focal length in meters)

When are f u and v positive?

1. f is positive if its converging

2. u is positive unless u wanna keep consistent convention with a previously defined thing

3. v is positive if its real

What is an axial ray and what property does it have?

Rays which enter the lens parallel to the principle axis. Axial rays form the image ON the focal point.

What is a non- axial ray and what property does it have?

They are rays that enter the lens NOT parallel to the principle axis. They form an image on the focal plane, NOT the focal point.

Is the focal length always symmetrical on either side of a lens?

Yes

What are the 2 ways of forming a virtual image?

Using a concave lens always forms a virtual image

Using a convex lens, and the image is formed IN FRONT of the focal point (closer to lens than focal point)

What is the focal length?

The perpendicular distance between the lens axis and the focal plane.

Advantages of reflecting telescopes

• Excellent Image Quality: Mirrors can be made thin (a few nanometres thick) and still provide excellent image quality, making them easier and cheaper to produce.

• No Chromatic Aberration: Mirrors reflect all wavelengths of light equally, avoiding the color fringing seen in refracting telescopes.

• Parabolic Mirrors Solve Aberrations: Spherical aberration in mirrors can be eliminated by using parabolic mirrors.

• Lightweight: Mirrors are lighter than lenses, making them easier to handle and adjust for astronomical observations.

• Better Support: Large primary mirrors can be supported from behind, preventing sagging or distortion due to weight.

• Composite Mirrors: Large mirrors can be constructed from smaller segments, as in the James Webb Space Telescope, allowing for massive apertures without the need for a single large piece of glass.

• Versatility: Reflecting telescopes are easier to manoeuvre and are well-suited for observing faint deep-sky objects due to their ability to gather more light.

Disadvantages of Refracting telescopes?

• Lens Purity: The glass used in the lenses must be pure and free from defects. Achieving this for large-diameter lenses is very difficult and expensive.

• Weight and Distortion: Large lenses are heavy and prone to bending or distorting under their own weight, reducing image quality.

• Chromatic Aberration: Lenses disperse light, causing chromatic aberration, where different colours focus at different points.

• Spherical Aberration: Imperfect lens shapes can lead to spherical aberration, distorting the image.

• Limited Support: Lenses can only be supported at their edges, making it challenging to stabilize and align large lenses.

• Heavy and Difficult to Move: Refracting telescopes are incredibly heavy and challenging to handle or reposition to follow celestial objects.

• Long Focal Length Requirement: Achieving high magnifications requires very large-diameter objective lenses with extremely long focal lengths, making the telescope bulky.

What type of telescope is most preferred in modern telescopes?

Reflecting

What is chromatic aberration?

For a given lens, the focal length of red light is greater than that of blue light, which means they are focused at different points (since blue is refracted more than red). This can cause a white object to produce an image with coloured fringing (coloured edges), with the effect being most noticeable for light passing through the edges of the lens.

Are reflecting telescopes affected by chromatic aberration?

What is spherical aberration?

When light is focused in different places due to the curvature of a lens or mirror, causing image blurring. This can be resolved in reflecting telescopes by using a parabolic mirror.

Difference between Refracting and Reflecting telescopes?

Refracting = lenses

Reflecting = Mirrors

What image is formed in a converging lens is used and the image is formed further away than the focal point? (2 marks)

Real

Inverted

What is the equation to work out the focal length? (The lens equation)

1/f = 1/u + 1/v

What does it mean about the image is v (image distance) is negative?

The image is virtual. This is because it means the image is forming on the same side of the object.

What is meant if an Astronomical telescope is in Normal Adjustment?

The 2 lenses (objective and eyepiece) share the same focal plane. Normal adjustment for a refracting telescope is when the distance between the objective lens and the eyepiece lens is the sum of their focal lengths (fo + fe ). This causes the principle focus is in the same position for both lenses

What does an astronomical telescope ray diagram look like?

What does aberration mean?

Deviation (not normal)

What can you assume if the object is assumed to be at infinity?

The light rays from the object enter the objective lens parallel (not always to principle axis!)

What are the 2 equations for angular magnification?

M = Fo/Fe = 𝜃i/𝜃o (where 𝜃i is the angle subtended by the image) (BOTH THETA’s must be less than 10 degrees!)

The larger number is ALWAYS on top!

Why must a refracting telescope be long in length and what are the problems with this? (3 marks)

Since the angular magnification is Fo/Fe, Fo must be large to achieve a good magnification level (Fe cannot be very small since it needs to form a magnified image which can be seen by a human)

This therefore requires a large length of telescope which is difficult to construct and they can sag easily since they can only be supported around the edges (since inside the radiation/light passes through)

This is difficult and requires a large building to store.

Why are radio telescopes much easier to construct than optical telescopes?

• They can be made from a wire mesh, which is cheaper and easier than using glass

• They can have a larger imperfections since wavelength of radiation is much bigger than radiation of visible light. (doesn’t have to be extremely precise)

What 2 lenses are astronomical refracting telescopes consist off?

Objective lens

Eye lens

What does the eye lens do?

Form a magnified virtual image

How does a reflecting telescope work?

Uses mirrors to reflect and focus the light.

Parabolic concave primary mirror converges axial rays from an object to its principle focus, forming an image.

An eye lens then magnifies this image, the same in refracting telescopes.

What is the reflecting telescope name and what is special about it?

Cassegrain arrangement.

It uses a convex secondary mirror to stop the observer blocking out incoming light.

Define the Rayleigh Criterion

Two objects can just 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.

How can you solve chromatic and spherical aberration in lenses?

Using an achromatic doublet

This is done using a convex lens and a concave lens of different types of glass cemented together.

What is a CCD?

Charge-Couple Devices, are very sensitive light sensors that capture images digitally.

How do CCD’s work?

Silicone chips with millions of pixels. When a photon hits one of these pixels, the photoelectric effect occurs, and electrons are liberated , causing a charge to accumulate on it.

This charge is then measured and used to create a digital signal. The signal describes the intensity and where the light hit.

How do radio telescopes work?

A parabolic dish focuses the radio waves onto a receiver (antenna). This signal is then amplified by a pre amplifier to make the weak radio signal stronger, without adding much extra noise. A tuner then allows wavelengths to be filtered out (e.g unwanted ones) and then this signal is sent to a computer to create a false-colour image.

How do radio telescopes achieve a lot higher resolving power than visible light, despite the wavelength of radio waves being a million times longer than visible light?

Linking lots of telescopes together, allowing many telescopes being able to form a single image.

Compare CCD’s with the human eye.

What precision does a dish for a radio telescope need to have to avoid spherical aberration?

𝜆/20

What is collecting power and what is it directly proportional to?

A measure on the ability of a lens or mirror to collect EM radiation.

Directly proportional to the area of the objective lens (d²)

Why is a larger colleting power important?

The greater the collecting power, the brighter the

images produced.

Why can radio wave dish’s be made much cheaper and easier? (2 marks)

They can be made our of wire mesh.

They don’t have to be as perfect as optical telescopes due to the longer wavelength.

Similarities and Differences between radio and optical telescopes?

Similarities

1. Function: Both telescopes intercept and focus incoming radiation to detect its intensity and produce images.

2. Parabolic Design: Both use a parabolic dish or mirror for focusing radiation—radio telescopes with a parabolic dish, optical reflecting telescopes with a parabolic mirror.

3. Mobility: Both types can be moved to focus on different sources of radiation or track a moving source.

4. Ground-Based Location: Both can be built on the ground since radio waves and visible light pass easily through the atmosphere.

Differences Between Radio and Optical Telescopes

1. Wavelengths:

   • Radio telescopes detect much longer wavelengths than optical telescopes, meaning they require different designs and sizes for effective resolution.

2. Size:

   • Radio telescopes need to be much larger in diameter than optical telescopes to achieve the same resolving power because of the longer wavelengths of radio waves.

3. Construction:

   • Radio telescopes use a wire mesh for their parabolic dish, which is cheaper and simpler to construct as long as the mesh size is less than λ/20\lambda/20λ/20. Optical telescopes require precision mirrors or lenses.

4. Image Formation:

   • Radio telescopes must scan across an area to build up an image, while optical telescopes form images instantly.

5. Interference:

   • Radio telescopes suffer from man-made interference (radio transmissions, phones, microwave ovens), whereas optical telescopes are affected by weather conditions, light pollution, and stray radiation.

6. Collecting Power:

   • Due to their larger objective diameter, radio telescopes have greater collecting power compared to optical telescopes, enhancing their ability to detect faint sources.

7. Applications:

   • Radio telescopes are often used for studying distant cosmic phenomena such as pulsars and quasars, while optical telescopes are better suited for observing visible objects like stars and planets.

Do both UV and IR telescopes use primary concave mirrors that focus the radiation onto a detector?

Yes

What are 2 difficulties that IR telescopes face and how do they overcome them?

• The telescope itself produces its own infrared emissions. Therefore, it must be cooled down to almost absolute zero.

• The atmosphere absorbs nearly all infrared radiation. These telescopes must be launched into space or be put on a weather balloon or aeroplane to be used effectively.

How do UV telescopes work?

Primary concave mirror that focuses radiation onto a detector (CCD)

The mirror must be more parabolic than optical telescopes due to UV having a smaller wavelength.

What are 3 reasons for putting telescopes into space?

• The atmosphere absorbs most of the electromagnetic spectrum, which is not useful if trying to capture it with telescopes

• Light pollution and other devices on Earth that can interfere with the telescopes (microwaves)

• The atmosphere alters the path of light as it passes through it.

Can CCD’s detect X-rays?

No, to do this you need to use X-Ray CCD cameras which are highly sensitive.

How do X-ray telescopes work?

The radiation is gradually altered in directed by nested mirrors. The X-rays reflect of these mirrors (graze them) and eventually they are focused on a detector. This is called a grazing telescope.

What are 3 ways to detect X-rays?

Modified Geiger counter

Fine wire mesh

Highly sensitive X-ray CCD cameras

What is 1 parsec in light years and what does this tell you about the size?

1parsec is 3.26 light years, meaning 1 parsec is larger than 1 light year.

How do you convert 20 pc to light years?

Since parsecs are larger than light years, MULTIPLY by 3.26 = (65.2 light years)

(1 parsec = 3.26 light years)

What is the definition of 1 parsec?

Distance from Earth that causes a parallax angle of 1 arcsecond

What is an astronomical unit?

1 AU is the MEAN distance between the Earth and the Sun (Mean distance since the Earth’s orbit is elliptical so its not constant the entire year)

What is 1 arcsecond in degrees?

1 arcsecond = 1/3600 degrees

The greater the angle of parallax, the closer or further away the star is?

Closer, since closer objects move more than further objects relative to Earth’s orbit.

Why do observatories take 2 images, 6 months apart to measure the parallax angle?

This method maximizes accuracy by using the largest possible baseline (the diameter of Earth's orbit, 2 AU).

What is the equation to work out the parallax angle, given the distance the object is and the distance between the earth and the sun (Au)

θ = r/d (where r is 1Au)

How can you convert arc seconds into radians?

1 arc second = 1/3600 degrees

1/3600 × 1 arc second x pi/180 = radians

What must θ be in the equation θ = r/d

θ in radians!

What is 1pc in meters?

3.08×10^16m

If using meters and ms^-1, what will your time be given in if using v = s/t

Seconds! So if its a big number don’t panic, just convert to years! (seconds/365×24×60×60)

What is the unit for parallax angle?

Arc seconds

What is the definition of a parallax angle?

Half the total angular shift by a star that appears to move relative to background stars in 6 months as the Earth moves from one end of its orbit to another.

The angle subtended by mars is 5 arcseconds. What angle would you use in theta = r/d given the radius?

2.5 arc seconds! In the diagram, a is HALF of the angle subtended from Earth to mars!

Definition of luminosity?

The power output of a star per second in all directions (a rate of energy transfer) (W)

Above what temperature do objects emit EM radiation?

Above absolute zero.

What type of EM radiations do objects at room temperature emit?

Infrared

What is a black body?

An object that absorbs all electromagnetic radiation for all wavelengths and can emit all wavelengths of electromagnetic radiation. They do not reflect or refract radiation.

Does a black body have to be black?

No!

Are stars ASSUMED to be a black body?

Yes, not actually is since a true perfect black body doesn’t exist.

What happens to the intensity and wavelength emitted by a body when its temperature increases?

BOTH intensity and wavelength increase

If the temperature of an object is increasing, what happens to the wavelengths emitted?

The smaller the wavelength emitted (Since the intensity has increased, and E = hc/lambda for a smaller lambda the larger the energy emitted)

Also due to Wiens displacement law (lambda = 2.9×10^-3 /T , as T increases, lambda decreases)

What is Wien’s displacement equation?

𝜆max = 2.9×10^-3 / T (mK - meters Kelvin NOT milli kelvin!!!!)

What are you assuming when you use the Wien displacement law?

The object is a black body

What is the units for Wien’s constant?

mK (meter Kelvin) since 𝜆 (m) x T (K)

What does 𝜆max represent in Wien’s law?

Peak wavelength

What is the peak wavelength?

𝜆max is the wavelength at which the maximum intensity (power recieved per area) occurs

Does a brighter star correspond to a hotter star?

No! Hotter stars produce wavelengths that may not be in the visible light spectrum.

What is Stefan’s law and what 2 things (which are the same) does it give you?

P/L = (5.67×10^-8)AT^4

Where A is surface area of black body

T is temperature in Kelvin

5.67×10^-8 is Stefan’s constant (Wm^-2T^-4)

What must be assumed for the inverse square law to be used about the power output of a star?

It outputs the same power in all directions (sun spots on the sun are cooler so will not output as much power)

What are Balmer lines?

The Balmer lines are specific spectral lines of hydrogen that appear in the visible region of the electromagnetic spectrum. They are part of the Balmer series, which describes the electron transitions in a hydrogen atom when an electron from n=2 is excited.

How are Balmer lines formed in absorption and emission spectra?

1. Balmer Lines in an Absorption Spectrum

• When light from a hot star passes through a cooler hydrogen gas (e.g., in the star’s outer atmosphere), the hydrogen atoms absorb specific wavelengths.

• This creates dark lines in the star’s spectrum at the Balmer wavelengths.

• Seen in most stars, including the Sun.

2. Balmer Lines in an Emission Spectrum

• When a gas cloud or nebula is heated (e.g., by a nearby star), the hydrogen atoms get excited and then emit light as electrons fall to lower energy levels.

• This produces bright lines at the Balmer wavelengths.

• Seen in hot gas clouds and nebulae.

What do the Balmer lines give an indication of a star?

The surface properties of a star - NOT its core properties.

Temperature of star