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JJFKCLM
032
– 27 –
N04/4/PHYSI/HP3/ENG/TZ0/XX+
H4. A student looks at two distant point sources of light. The wavelength of each source is 590 nm.
The angular separation between these two sources is 3.6 s104 radians subtended at the eye. At
the eye, images of the two sources are formed by the eye on the retina.
(a)
State the Rayleigh criterion for the two images on the retina to be just resolved.
[2]
.....................................................................
.....................................................................
.....................................................................
(b)
Estimate the diameter of the circular aperture of the eye.
[1]
.....................................................................
(c)
Use your estimate in (b) to determine whether the student can resolve these two sources.
Explain your answer.
.....................................................................
.....................................................................
.....................................................................
8804-6503
[2]
– 30 –
M05/4/PHYSI/HP3/ENG/TZ2/XX+
H3. This question is about optical resolution.
The two point sources shown in the diagram below (not to scale) emit light of the same
frequency. The light is incident on a rectangular, narrow slit and after passing through the slit,
is brought to a focus on the screen.
A
B
light sources
slit
screen
Source B is covered.
(a)
Using the axes below, draw a sketch graph to show how the intensity I of the light from A
varies with distance along the screen. Label the curve you have drawn A.
[2]
I
distance along the screen
Source B is now uncovered. The images of A and B on the screen are just resolved.
(b)
Using the same axes as in (a), draw a sketch graph to show how the intensity I of the light
from B varies with distance along the screen. Label this curve B.
[1]
(This question continues on the following page)
2205-6515
– 31 –
M05/4/PHYSI/HP3/ENG/TZ2/XX+
(Question H3 continued)
The bright star Sirius A is accompanied by a much fainter star, Sirius B. The mean distance
of the stars from Earth is 8.1s1016 m. Under ideal atmospheric conditions, a telescope with an
objective lens of diameter 25 cm can just resolve the stars as two separate images.
(c)
Assuming that the average wavelength emitted by the stars is 500 nm, estimate the
apparent, linear separation of the two stars.
[3]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
Turn over
2205-6515
– 30 –
N05/4/PHYSI/HP3/ENG/TZ0/XX+
H4. This question is about resolution.
(a)
State the Rayleigh criterion for the images of two point sources to be just resolved.
[2]
......................................................................
......................................................................
......................................................................
A man is walking along a straight path at night towards two light sources as shown below.
light
sources
path
man
not drawn to scale
When the man is 150 m from the sources, the images of the two sources are just resolved by his
eye. The wavelength of the light from each source is 590 nm and the diameter of the aperture
of his eye is 5.0 mm.
(b)
Estimate the distance between the two sources.
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
8805-6503
[3]
– 31 –
M06/4/PHYSI/HP3/ENG/TZ2/XX+
H5. This question is about the Rayleigh criterion.
(a)
Light from two monochromatic distant point sources, S1 and S2, is incident on a narrow
slit. After passing through the slit, the light is incident on a screen.
S1
S2
slit
screen
On the axes below, draw the intensity distribution of the diffracted light on the screen
from each source when the images of S1 and S2 are just resolved according to the Rayleigh
criterion.
[3]
intensity
position
(b)
A woman views an approaching car at night. The apertures of her eyes are each of
diameter 3.0 mm. The headlamps of the car are separated by a distance of 1.2 m and emit
light of wavelength 400 nm.
Calculate the distance of the car from the woman at which the images of the two
headlamps are just resolved.
.......................................................................
.......................................................................
.......................................................................
.......................................................................
.......................................................................
2206-6515
3131
[3]
– 30 –
N06/4/PHYSI/HP3/ENG/TZ0/XX+
H3. This question is about resolution.
Monochromatic light from two identical point sources is incident on a narrow slit as shown
below (not to scale). After passing through the slit, the light is brought to a focus on a screen.
point sources
slit
screen
The images of the two sources on the screen are just resolved according to the Rayleigh
criterion.
(This question continues on the following page)
8806-6503
3032
– 31 –
N06/4/PHYSI/HP3/ENG/TZ0/XX+
(Question H3 continued)
The diagram below shows the intensity distribution on the screen of the light from one of the
point sources.
intensity / arbitrary units
distance along screen / arbitrary units
(a)
(b)
On the diagram above, draw the intensity distribution on the screen of the light due to the
second source.
[2]
The planet Pluto is 4.5s1012 m from Earth and the diameter of Pluto is 2.3s106 m. The
average wavelength of the light received by the Earth from Pluto is 500 nm.
Deduce, whether the human eye should be able to see Pluto as a disc or only as a point
source of light.
[3]
.......................................................................
.......................................................................
.......................................................................
.......................................................................
.......................................................................
Turn over
8806-6503
3132
– 28 –
M07/4/PHYSI/HP3/ENG/TZ2/XX
H3. This question is about diffraction and resolution.
Blue light of wavelength 450 nm from a star passes through a telescope with a circular aperture
of 0.25 m and forms an image on a photographic plate 0.75 m from the focussing lens.
(a)
(i)
(ii)
In the space provided below, draw a labelled sketch to show the diffraction fringe
pattern produced on the photographic plate.
[2]
Calculate the diameter of the central maximum on the photographic plate.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
(This question continues on the following page)
2207-6515
2829
– 29 –
M07/4/PHYSI/HP3/ENG/TZ2/XX
(Question H3 continued)
(b)
The telescope in (a) is now pointed at two stars.
The maximum separation of the stars is d and they are both 1.5 % 1017 m from the
telescope.
(i)
Determine the separation d of the stars such that the images of the stars are just
resolved in light of wavelength 450 nm.
[3]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
Over a period of time the separation of the stars varies from
d
to 2d.
2
Describe and explain the changes to the image produced by the telescope during
this time. You should include diagrams to illustrate your answer.
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
2207-6515
2929
[3]
±±
M09/4/PHYSI/HP2/ENG/TZ1/XX+
(Question B4 continued)
Part 2
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[3]
(This question continues on the following page)
2209-6508
2830
±±
M09/4/PHYSI/HP2/ENG/TZ1/XX+
(Question B4, Part 2 continued)
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