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ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿposition P and again when it is
in position Q.
Explaining your reasoning, draw in the two boxes (i) and (ii) the same
part of the spectrum of star A when it is at P and Q, respectively.
(for reference, the dotted lines in boxes (i) and (ii) show the same
spectrum as in figure 2)
(5)
(b) (i) The calcium K line from a laboratory source has a wavelength of
3.9342 x 10-7 m. The same line, when measured in the spectrum of star A,
when A is in position S in figure 1, has a wavelength of 4.7804 x 10-7 m.
Calculate the velocity of the binary system.
(ii) The wavelength of the same calcium K line, when measured in the
spectrum of star A as it orbits, varies from a maximum of 4.7936 x 10-7 m
to a minimum of 4.7672 x 10-7 m over an interval of 120 days. Calculate
the radius of the orbit.
(7) = (12)
PH04 February 1996
1. (a) By means of separate ray diagrams, show how the principal focus
of a thin converging lens and the principal focus of a thin diverging
lens are defined.
(2)
(b) A small object is placed on the principal axis and 250 mm from a thin
diverging lens of focal length 200 mm.
(i) Calculate the distance of the image from the lens.
(ii) State whether or not the image is on the same side of the lens as
the object.
(3) = (5)
2
(a) The figure shows the cross-section of a step-index optical
fibre. Using the axes provided, draw a sketch graph showing how the
refractive index varies with the distance r from the centre of the core
to a point well outside the cladding. Indicate clearly on your graph the
interfaces between the core and cladding and between the cladding and
air.
(3)
(b) Give two reasons. apart from cost, why it is advantageous to transmit
signals optically through thin glass fibres rather than electrically
through thin copper wires.
(2) = (5)
3
(a)
(i) Explain what is meant by the quantum efficiency of a
detector.
(ii) Give approximate values of the quantum efficiency of a charged
couple device (CCD), a photographic film and a human eye.
(3)
(b) Describe the mode of action of a CCD used as a detector in a
telescope.
(5) = (8)
4 (a) State, for black body radiation (defining the symbols used),
(i) Wien's displacement law:
(ii) Stefan's law:
(3)
(b) Using the axes below, sketch radiation curves for a black body at
three different temperatures. Indicate on your graph which curve has the
highest temperature.
(c) The spectrum of a star has its intensity maximum at a wavelength of
500 nm. Assume that the star is a perfect black body of radius 5.90 x 108
m.
(i) Calculate the temperature of the surface of the star.
(the Wien constant = 0.0029 m K)
(ii) Calculate the total power radiated by the star.
(the Stefan constant = 5.67 x 10- W m-2 K-4)
(4) = (10)
5. (a) Emission from stars and galaxies covers most of the
electromagnetic spectrum.
(i) Radio waves of certain frequencies emitted by galaxies cannot be
observed on Earth. Explain why this is so.
(ii) Ultraviolet radiation from stars cannot be detected on Earth.
Explain why this is so and suggest how such radiation may be detected.
(3)
(b)
(i) Explain why the wavelengths used in radar astronomy are
confined to the range 1 cm to 20 cm.
(ii) Describe how radar astronomy is used to measure the distance between
a planet and Earth.
(5)
(c)
(i) In the course of their orbits, the distance between the Earth
and Venus changes. The radii of the orbits of the Earth and Venus are 1.5
x 108 km and 1.1 x 108 km respectively. If a radio pulse is transmitted
from Earth towards Venus, calculate the greatest and least times that
would be measured before the return pulse was detected.
(ii) Explain why radar cannot be used to take measurements of a star such
as Alpha Centauri which is at a distance of 1.3 parsec from Earth.
(5) = (13)
6 .(a) State what is meant by parallax.
(2)
(b) (i) Define the parsec.
(ii) With the aid of a diagram explain the principles underlying the
trigonometric parallax method of stellar-distance measurement.
(iii) State a correction which has to be made to the measurements.
(7)
= (9)
7 Hubble's law relates the speed of recession of a galaxy to its distance
from Earth. The Hubble constant is taken to have a value within the
limits of 50 km s-1 Mpc-1 and 100 km s-1 Mpc-1
(a) Give one reason why there is such a large uncertainty in the value of
the Hubble constant.
(b) Show how the maximum distance to the edge of the Universe may be
obtained from Hubble's law.
(c) When estimating the age of the Universe, what is the significance of
the lower limit of the Hubble constant?
(5) = (5)
PH04 - March 1997
1. A student looks at a clock through
of the lens is 0.30 m and the distance
m.
(a) Calculate the distance between the
(2)
(b) Calculate the linear magnification
(2) = (4)
a diverging lens. The focal length
from the lens to the clock is 4.2
lens and the image of the clock.
produced by the lens.
2
(a)
(i) State the type of cells in the retina of the human eye
that are of particular use in seeing in dim light.
(ii) State the approximate time it takes the eye to adapt from bright
light to dim light.
(2)
(b) Three slide transparencies, each of different but uniform density,
are placed in turn in a projector and the images produced on a screen are
viewed. The intensity of the image produced by the second transparency is
ten times as great as that produced by the first, and the intensity of
the third image is one hundred times as great as that produced by the
first. Given that response of the eye is proportional to log10
(intensity), complete the table.
relative intensity Log10 (relative intensity) response of the
eye 10 1 initial response R 100
1000
(2) = (4)
3 (a) An astronomical telescope consisting of two thin converging lenses
of focal lengths fo and fe respectively, is set up in normal adjustment
to view a distant object such as the Moon.
(i) Show, by means of a labelled ray diagram, how a magnified image is
formed by the instrument. Your diagram should show the paths through the
telescope of two non-axial rays from the Moon.
(ii) Given that the angular magnification of the instrument is given by
M =
angle subtended at the eye by the image (alpha’)
angle subtended at the eye by the object (alpha)
mark on your drawing the angles alpha and alpha’
(iii) An observer, with the aid of an astronomical telescope, can just
resolve two points on the Moon, which have an angular separation of 4
seconds of arc. The observer's unaided eye has a resolving power of 2
minutes of arc. Calculate the angular magnification of the telescope.
(7)
(b) A parallel beam of monochromatic light, incident on a converging
lens, fills the lens aperture completely. After transmission through the
lens the light falls on a plane surface placed parallel to the plane of
the aperture and approximately 1m away from it. The plane surface is in
the focal plane of the lens.
(i) Sketch the graph which shows how the intensity of the light falling
on the surface varies as the distance from the central axis of the lens
for distances close to the axis.
(ii) Hence, with the aid of a diagram, describe Rayleigh's criterion for
the resolution of two point sources viewed through a lens.
(5)
(c) State, without using mathematical equations, what is meant by the
resolving power of an astronomical telescope. Hence indicate how the
resolving power of a telescope is linked to the angular magnification of
the same instrument. (2) = (14)
4
(a) A parallel beam of light which contains red light and blue light
only, is incident on a converging lens of focal length fo By means of a
labelled ray diagram, show how chromatic aberration occurs. Indicate fo
on your diagram.
(3)
(b) The parallel beam of light in (a) is changed for a parallel
monochromatic beam. Show, with the aid of a diagram, how spherical
aberration occurs.
(2)
(c) State which one of the above aberrations occurs when white light is
incident on a concave mirror. (1) = (6)
5. (a) A radio telescope with a reflecting dish of diameter d, receives
signals from a galaxy. Explain why the power of the signal received by
the telescope is proportional to d2
(2)
(b)
A particular radio telescope receives 1.0 x 10-20 W m-2 from a
galaxy. Calculate the diameter of the telescope dish if the total power
received is 2.5 x 10-18 W.
(2) = (4)
6 (a) The
M100. The
curves of
shows the
Hubble Space Telescope was used to study the spiral galaxy
resulting images allowed astronomers to measure the light
the most distant Cepheid variable stars ever observed. Figure 1
variation of the apparent magnitude with time for such a star.
Use figure 1 to estimate
(i) the period of the variable star,
(ii) the mean apparent magnitude of the star. (2)
(b) Figure 2 shows the absolute magnitude as a function of the period for
a group of such variable stars.
(i) Use figure 2 to estimate the absolute magnitude of the star referred
to in part (a).
(ii) Hence calculate the approximate distance to this star.
(4) = (6)
7 (a) Sketch a Hertzsprung-Russell diagram, labelling the approximate
positions of Main Sequence stars, Red Giant stars and White Dwarf stars.
Indicate values of absolute magnitude and temperature on the axes. Label
the approximate position of the Sun on your diagram.
(5)
(b) The evolution of a star on the Main Sequence depends on its mass. It
could end up as a White Dwarf, a Neutron star or a Black Hole.
(i) Give three properties of White Dwarfs.
(ii) Compare the densities of White Dwarfs, Neutron Stars and Black Holes
and hence explain why Black Holes are so named.
(6) = (11)
8
(a)
(i) Describe how the motion of galaxies varies with their
distance from Earth.
(ii) Hence explain why astronomers will never be able to record the
presence of galaxies beyond a certain distance from Earth.
(4)
(b) Using data from the data book, calculate the distance to a given
galaxy if the speed of recession of the galaxy is 3.7 x 107 m s-1.
(2) = (6)
objective
eyepiece
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