9. Astrophysics Flashcards
What is the axis of symmetry called?
The principal axis
What is the principal focus?
A point on the axis which is the same distance from the optical centre as the focal length. This is where light rays travelling parallel to the principal axis prior to refraction converge.
Define focal length
The distance between the centre of the lens and the principle focus
What does ‘u’ represent in lens diagrams and equations?
The distance between the object and the centre of the lens, u is always positive
What does ‘v’ represent in lens diagrams and equations?
The distance between the image and the centre of the lens, v is positive for real images and negative for virtual images
Draw the ray diagram for an object that is a long way from the lens (beyond 2F) and describe the image’s appearance
The image is real and inverted but smaller than the object - this is called diminished
6.
Draw the ray diagram for an object that is very close to the lens and describe the image’s appearance
The image is virtual and upright but bigger than the object - this is called magnified
7.
Draw the ray diagram for an object that is fairly close to the lens (Between f and 2f) to the lens and describe the image’s appearance
The image is real and inverted but bigger than the object - this is called magnified
8.
Draw the ray diagram for an object that is at 2f and describe the image’s appearance
The image is real and inverted but the same size
9.
What does normal adjustment in a telescope look like?
10.
Give the formula for angular magnification in normal adjustment
M = angle subtended by image at eye ÷ angle subtended by object at unaided eye
Can also be written as M = 𝛼 / ß
State the equation that relates M to the focal length for objective and eyepiece lenses
M = fo / fe
This can only be used if both angles from M = 𝛼 / 𝛽 are less than 10º
How does an astronomical refracting telescope work?
There are two converging lenses, the objective lens and the eyepiece lens. The role of the objective lens is to collect light and create a real image of a distant object. This image is then magnified by the eyepiece lens, which produces a virtual image (formed at infinity so as to reduce eye strain when looking between the object and the telescope image).
What is chromatic aberration?
A lens refracts different colours of light by different amounts as they have different wavelengths. This causes the image for each colour to form in a slightly different position, causing coloured fringes around the image
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.
Describe a solution to chromatic and spherical aberration in lenses.
Using an achromatic doublet brings all rays of light into focus in the same position by using a convex lens and a concave lens of different types of glass cemented together.
State 3 advantages of reflecting telescopes
- There is very little chromatic aberration (only in the eyepiece lens, but this can be resolved by using an achromatic doublet)
- Simpler to increase the size of the objective since mirrors can be supported from behind and are lighter than lenses
- Using parabolic mirrors stops spherical aberration
What happens when you increase the size of the objective lens/mirror?
Increasing the diameter of the objective means you can observe fainter objects. This is because collecting power is proportional to (objective diameter)^2
Define the Rayleigh Criterion
‘Two objects will be just resolved if the centre of the diffraction pattern of one image coincides with the first minimum of the other’.
θ ≈ λ / D
What is apparent magnitude and absolute magnitude?
Apparent magnitude (m): how bright the star appears from Earth
Absolute magnitude (M): how bright the star would appear if it were placed 10 parsecs from Earth.
m-M=5log(d/10) (where d = distance from Earth)
What is the Hipparcos scale?
The Greek astronomer Hipparchus catalogued stars, defining their brightness in terms of apparent magnitudes (m), with brightest stars a magnitude of 1 and the faintest a magnitude of 6.
The scale has since been extended to include brighter objects (like the Sun, with an m of -26.47) and fainter objects that were discovered with the invention of the telescope.
Define parsec
The distance to an object that subtends an angle of one arcsecond (1/3600th of a degree) to the line that runs from the centre of the Earth to the centre of the Sun
Define light year
A light year is the distance travelled by light in a vacuum in one year. In metres this is 9.46 x 1015 m (speed of light multiplied by the number of seconds in a year)
State Stefan’s law
The power output of a star is directly proportional to its surface area and it’s (absolute temperature)^4
P = σ A T^4, where A = surface area (m^2), T = temperature (K) and σ = the Stefan constant = 5.67 x 10^-8 W m^-2 K^-4
State Wien’s displacement law
The wavelength of a star’s emission at peak intensity is inversely proportional to its absolute temperature.
λmax T = 2.898 x 10^-3 m k
(note: unit is metres Kelvin, not milliKelvin)
What are supernovae? Describe how type Ia and type II form
A supernova is the explosion of a star, which causes it to very suddenly and rapidly increase in absolute magnitude.
Type Ia Supernova: The result of a white dwarf core accumulating too much matter from its binary partner and exploding above a critical mass
Type II Supernova: A single star (for example a red giant) that collapses rapidly under its own gravity, causing its outer layers to be ejected
Explain why Type II supernovae cannot be used as standard candles whereas Type Ia supernovae can.
A standard candle is an astronomical object that has a known absolute magnitude so astronomers can calculate the distance using m - M = 5log(d/10). All Type Ia supernovae explosions have the same peak absolute magnitude (approximately -19.3) as they all have the same critical mass (thus have consistent light curves) so they can be used as standard candles. Type II supernovae are not as predictable, so they cannot be used as standard candles.
Draw the light curve of a typical type Ia supernova
Light curves are graphs of absolute magnitude against time since peak magnitude. The peak magnitude of a type Ia supernova is -19.3.
11.
What is the Doppler effect?
The change in wavelength and frequency of a wave as the source moves away or towards the observer.
As the source moves towards the observer, the waves are compressed and wavelength decreases. As the source moves away from the observer, the waves spread out and the wavelength increases.
∆λ / λ = - V / C = - ∆f / f
What is red shift?
Red shift (z) is the shift in wavelength and frequency of waves from a retreating source towards/beyond the red end of the electromagnetic spectrum. Cosmological red shift is evidence for the Big Bang. The formula for red-shift can only be used when v is much smaller than c (the speed of light).
State Hubble’s law
The velocity of receding galaxies is proportional to their distance from Earth.
v = H。d
v = velocity of a retreating galaxy (km s-1) d = Distance from Earth (Mpc) H。= Hubble’s Constant = 65 km s-1 Mpc-1
Use Hubble’s law to estimate the age of the universe.
Time = distance / velocity = 1 / H。(since v = H。d)
The units of Hubble’s constant must be converted to SI units
65 km s-1 Mpc-1 x 10^3 gives H。 = 65,000 m s-1 Mpc-1
Divide by 1 Mpc (3.08 x 10^22 m) to get the units for H。as s-1
H。= 2.11 x 10^-18 s-1 so 1 / H。= 4.74 x 10^17 s
Age (convert to years) = 4.74 x 10^17 / 3600 / 24 / 365 = 1.5 x 10^10 years (or 15 billion years).
Draw a simplified light curve for a binary star system.
12.
What are exoplanets?
Exoplanets are planets that are not in our solar system.
Direct observations of exoplanets are difficult as their light is often obscured by the stars they orbit. Also they tend to be too close together for the telescope to resolve
them.
How can we detect exoplanets?
- Radial Velocity Method: A star and a planet will orbit their common centre of mass, this means the star will have tiny variations in its distance from Earth, shown by tiny red and blue shifts in its spectrum.
- Transit method: As a planet moves between the star it orbits and the Earth, the star’s brightness appears to decrease slightly. We can detect this and use it to calculate the diameter of the planet. Unfortunately there is a low chance of this orbit being in the right place for us to measure this, so it is mostly only useful for detecting planets with small orbits (they are more likely to cross the star’s disc)
Draw the light curve for an exoplanet transiting in front of its star
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