Astrophysics Flashcards
What happens to light as it passes through a convex lens
The changing of the light rays direction are due to the fact that light travels slower than in glass than air. This effect is known as refraction
Complete diagram to show action of converging lens on a parallel beam of light, not parallel to the principal axis. Label principal focus F and label focal length f
Complete diagram to show action of converging lens on a parallel beam of light, not parallel to the principal axis. Label principal focus F
Complete the diagram
If rays from a point on the object actually arrive at one point to form an image, then the image is said to be?
give an example of image formed by a converging lens
a real image
- example of this type of image formed by a converging lens is when lens is used by magnifying glass
If rays from a point on the object actually only appear to have come from one point to form an image, then the image is said to be?
- give an example of an image formed by a converging lens
virtual
An example of this type of image formed by a converging lens is when the lens is used as a refractive telescope
How big an object or image looks to the eye depends on the?
angle to which it is subtended to at the eye
equation for angular magnification
angle subtended by image at eye / angle subjected by object at unaided eye
What can you say about the rays from objects with a very long distance
then rays from one point on the object are almost parallel. (Points are small and close to the eye)
Use constructional rays to find position and properties of image formed by a converging lens of an object at infinity
what does an object at infinity with a large (objective) lens form
a real, inverted, diminished image at its principal focus
equation for angular magnification and equation for length of telescope
length = fo + fe
M = fo / fe
A refracting astronomical telescope has a magnifying power (same as angular magnification) of 40 and a length of 820 mm. What is the focal length of each lens?
fo / fe = 40
fo + fe = 820
solve simultaneously to get
fo = 800 mm
fe = 20 mm
draw a diagram to show a parabolic mirror fixing spherical aberration
One way of using a converging mirror uses an additional convex mirror and an eyepiece.
You need to show the paths of two rays in a Cassegrain up to the eyepiece
What is dispersion
when refractive index of light varies with wavelength
do refracting and reflecting telescopes suffer from chromatic aberration
refractors will unless corrected
reflecting telescopes will not due to their primary mirrors
Advantages and disadvantages of reflecting and refracting telescopes
What is the minimum angular resolution of a telescope (resolving power), and what is it measured in
The minimum angular resolution of a telescope is the minimum angular separation which the instrument can resolve - i.e. distinguish.
measured in radians, not watts
Sketch the appearance of a diffraction pattern caused by a small circular hole in front of a laser and underneath it a sketch graph of the variation in intensity in one direction.
How do you increase the collecting power
increase diammeter of the object
as collecting power is proportional to (diammeter)^2
Similarities and differences between radio telescopes and optical telescopes
be ground-based because the atmosphere is transparent to a large range of radio wavelengths. Compared to an optical telescope, a radio telescope has a low angular resolution because of the dependence on wavelength in the Rayleigh criterion, θ ≈ λ /D
Unlike optical telescopes, radio telescopes can operate during the day as well as at night
Limitations of ground based telescopes
atmospheric absorption and distortion in the visible region of the electromagnetic spectrum are limiting factors in image
Ozone, oxygen, water vapour and carbon dioxide all contribute to the absorption of light, from the ultraviolet through visible to infrared. Dust within the atmosphere also absorbs and scatters light on its way to the telescope, and atmospheric turbulence (due to convection currents) reduces image quality. Such problems are avoided by building observatories in dry, pollution-free areas at high altitude, or, better, by putting telescopes in orbit around the Earth beyond the atmosphere
What are infrared telescopes used for
used to make observations of cool regions
What are UV telescopes used for
Ultraviolet (UV) telescopes are used to examine objects in the UV part of the electromagnetic spectrum
Explain what is meant by the Rayleigh criterion
Explain what is meant by the Rayleigh criterion
(Minimum angle is when) the central maximum of (the diffraction pattern of light from) one object coincides with the first minimum of (the diffraction pattern) of
the second object.
What you need to know for a CCD
- quantum efficiency of CCD is higher than that of an eye
- resolution of CCD higher
- The CCD is better for scientific purposes (e.g., astronomy, detailed imaging) due to its high quantum efficiency and resolution.
The eye excels in convenience for real-time use but is limited in its detection and storage capabilities.
Define quantum efficiency
Quantum efficiency is the ratio of the number of photons detected to the number of photons incident on the detector.
Define resolution
Resolution refers to the ability to distinguish between closely spaced objects or details.
A telescope uses wavelengths in the range 90 nm to 120 nm.
Explain why this telescope must be located in space.
Go on to discuss one advantage that this telescope has compared to a telescope with the
same aperture that uses visible light.
Wavelengths in the range 90 nm to 120 nm fall within the ultraviolet (UV) region
- Which is absorbed by (ozone in) the atmosphere so must be in space
- UV light gives better resolution, as it has shorter wavelength, eqaution linked is theta = wavelength / diammeter
one telescope has a spherical disc shape and another has a parabolic disc shape. State which telescope will produce a more detailed image
Parabolic as it has no spherical aberration
Two telescopes have different diammeters. Which one would be better at resolving images of two objects that are closer together
One with larger diammeter because its minimum angular resolution depends on 1/D
A spacecraft passes Pluto at a distance of 12 500 km. The telescope on board has an aperture of diameter 0.21 m and operates at a wavelength of 450 nm.
Discuss whether this telescope is suitable for studying a crater with a diameter of approximately 1 km on Pluto.
Theta = wavelength / d
= 2.14 x 10^-6 rad
smallest detail = 2.14 × 10^−6 × 12.5 × 10^6 = 27 m
The telescope can resolve features as small as 27 m, which is much smaller than the diameter of the crater, 1km. Telescope is suitable
How do you work out the collecting power when given diammeter
power is proportional to area
so calculate area to find power
problems of refractors vs reflecting
Can suffer spherical aberration and chromatic aberration.
Reflecting are lighter. Reflecting are shorter. Mirrors do not suffer
from chromatic aberration.
problems of reflecting telescope
Spider/secondary mirror block some of the light/reduce image
brightness/cause diffraction effects.
The Griffith telescope is used to observe two point objects which subtend an angle of 1.8 × 10^–6 rad at the unaided eye.
The typical human eye has a minimum angular resolution of approximately 3.2 × 10^–4 rad
Calculate the focal length of the eyepiece lens so that an observer can just resolve the two
objects when observing them through the Griffith telescope. focal length 5.03 m
M = 3.2 × 10^–4 / 1.8 × 10^–6
= 178
fe = fo / M
fe = 5.03 / 178
The asteroid Apophis has a diameter of 325 m
It has been calculated that, in 2029, its distance of closest approach to the Earth’s surface
will be 3.0 × 10^4 km
The Griffith telescope may be used to view Apophis using the eyepiece lens of 1.8 x 10^6 rad
Deduce whether this telescope is suitable to obtain a detailed view of Apophis.
Support your answer with a calculation.
What are the shapes of the primary and secondary mirrors in a Cassegrain telescope?
primary : concave
secondary : convex
The Triesnecker Crater on the Moon has a diameter of 23 km. Calculate the angle subtended by the image of this crater when viewed through a telescope of angular magnification 50 on the Earth.
distance from Earth to Moon = 3.8 × 10^5 km
s = r x theta
theta = 23 / 3.8 x 10^5 = 6.053 x 10^-5
M = theta 2 / theta 1 = to give θ2 = 50 × θ1 = 3(.026) × 10–3 (rad)
what is the ratio of resolving power of reflector / resolving power of refractor
Theta reflector / theta refractor = d refractor / d reflector
Give two reasons why the secondary mirror in the Cassegrain telescope affects the clarity of the image.
- mirror blocks light so less light hits objective mirror
- light diffracted passing secondary mirror affects image
The Moon is 380 000 km from the Earth and has a diameter of 3 500 km. Calculate the angle subtended by the image of the full Moon when viewed through the telescope. Telescope made from two cardboard tubes of slightly different diameter, two convex lenses of focal lengths 0.10 m and 0.50 m respectively
fo / fe = 5
5 x 3500 / 380 000 = 0.046 rad
The telescope suffers from chromatic aberration. Describe how this affects the appearance of an image.
edges on image will appear coloured
Huygens made an astronomical telescope with an angular magnification of approximately 100. Using this telescope, Huygens discovered Titan, a satellite of Saturn. At this angular magnification, the image of Titan subtends an angle 4.0 × 10–3 radians when it is approximately 1.3 × 109 km from the Earth. Calculate the diameter of Titan.
(4 x 10^-3) / 100 = 4 x 10^-5
a = d / r
d = 5.2 x 10^4 km
State and explain two optical advantages reflecting telescopes have compared with refracting telescopes.
no chromatic aberration - mirrors do not refract light (1) no spherical aberration - use of parabolic mirror (1) no distortion - mirror can be supported more strongly (1) better resolving power or greater brightness - mirrors can be larger (1) more light gets through (image brighter) - lens absorbs more light (1)
A telescope is made from two converging lenses of focal lengths 2.50 m and 0.020 m. The telescope is used to observe a planet which subtends an angle of 5.0 × 10–5 rad at the objective. Calculate the angle subtended at the eye by the final image.
M = 2.5 / 0.02 = 125
125 x 5.0 × 10–5 = β = 6.2(5) × 10–3 rad
Convex mirror between objective and F1
State what is meant by chromatic aberration and explain the effect it would have on the image in an uncorrected refracting telescope.
chromatic aberration -different wavelengths (1) refracted different amounts or different speeds in glass (1) image with coloured edges or different focus for different colours (1)
Explain why the Cassegrain telescope would be almost free of chromatic aberration.
no refraction (by mirrors), as telescopes use mirrors. some chromatic aberration in eyepiece lens
Q2.1 How many times brighter is a fourth magnitude star than a fifth magnitude star?
Q2.2 How many times brighter is a fourth magnitude star than a sixth magnitude star?
Q2.3. How many times brighter is a second magnitude star than a ninth magnitude star?
What is 3.1416° expressed using minutes and seconds?
- don’t fill in the blanks, Q3.3 is find value of tan(1’’)
Two stars, i and q, in the constellation of Auriga appear equally bright, but i is known to be at a distance of 330 light-years from us, and q is 108 light-years away. Which star is the most luminous and by how many times?
What two basic assumption have been made in this section?
Assumptions :
- there is no absorption of light in the space looked at
- the radiation is isotropic (same in any direction)
apparent magnitude of betelgeuse is 0.45 and absolute magnitude is -5.47. How far away in light years is betelgeuse. State an assumption you have made
There has been no light absorption in space
Sketch a graph of lambda max against T.
Consider two stars of black body temperatures T1 and T2. If the ratio of their power output (P1/P2) is known, show how Stefan’s law can be used to calculate the ratio of their diameters, d1/d2
Draw the hertzsprung-Russel (H-R) diagram
a)
W - protostar / gas cloud
X - main sequence star
Y - Red giant
Z - White dwarf
Theta Carinae is a star with a radius five times that of the Sun. It has a surface temperature of 31
000 K. The astronomer suggests that the Earth-sized planet receives a similar amount of power
from Theta Carinae as the Earth does from the Sun.
The average power output of the Sun is 3.8 × 10^26 W.
Determine the orbital radius of the Earth-sized planet orbiting Theta Carinae.
Colour of Schaefer = orange
Colour of Caph = white
- Use Wiens law to calculate temperature
For Caph = T = 2.9 x 10^-3 / 410
x 10^-9 = 7250 Kelvin
For Schedar = T = 2.9 x 10^-3 / 660 x 10^-9 = 4400 Kelvin
Schedar has longer wavelength hence it has a more redder colour
The temperatures match the spectral class colour
As Caph is in spectral class F & Schedar is in spectral class K
D
- make sure you remember the point at which it peaks as you will have to remember this graph.
b) Explain, with reference to the SI units involved, how the curve you have drawn can be used to determine the black-body temperature of the star.
for a) just draw a single peak
b) Use peak wavelength and sub into Wiens law equations. Temperature must be measured in Kelvin, wavelength in metres
The Hipparcos scale is another name for what diagram? Give a picture of what it looks like
Hertzsprung-Russel diagram
e) A star much more massive than the Sun may become a supernova and then a black hole.
Discuss whether supernovae and black holes can be placed on the HR diagram in.
e) - Absolute magnitude of supernova (is about –20), beyond scale of HR diagram
- Supernova is shortlived / varies so cannot be assigned a position
- Temperature of a supernova (peak) is too high (greater than 50 000 K)
- Black hole – escape velocity greater than c
- no light emitted /absolute magnitude too dim to fit on scale
- Temperature of a black hole would be too low (less than 2500 K
Which star has the brightest absolute magnitude
Rasalgethi
- don’t focus on which is the largest number but which is the most negative (highest negative)
- get help on it just in case
A) which of the three stars appear the brightest
B) deduce which of the 3 stars is the largest
A) lowest value of apparent magnitude indicates brightest star, Vega has lowest so it brightest
B) - similar temperature, bigger absolute magnitude, due to stefans law equation, to have greater p power, must have greatest area
State which star is closer to earth
Sirius
- Sirius is 10pc away as apparent magnitude = absolute magnitude
- Data shows Regel would appear brighter if at 10pc but is seem to be dimmer
- it appears brighter even though it has a lower luminosity / lower surface temperature
P
- lowest peak wavelength
- wavelengthmax x temperature = constant, so the lower the wavelenght, the higher the temperature
- has highest peak intensity, Use stefans law equation to see that higher intensity / power, higher temp
0.5, 1, 1.5, 2
Notice the units not in its usual nanometres.
Assuming power output of Arcturus is 100 times greater than that of the sun, show that’s its surface area must be approximately 200 times greater
A) is likely to be orange in colour
B) appears brightest from earth
A) sheddir: class K towards red end
B) Sheddir, had lowest value of apparent magnitude
