1. This question is about resolution.
(a) State the Rayleigh criterion for the images of two point sources to be just resolved.
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(2)
A man is walking along a straight path at night towards two light sources as shown below.
l i g h t s o u r c e s
p a t h m a n
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.
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2. This question is about wave phenomena and the particle nature of light. Travelling waves
(a) Graph 1 below shows the variation with time t of the displacement d of a travelling
(progressive) wave. Graph 2 shows the variation with distance x along the same wave of its displacement d.
t / s
x / c m 4 2 0 – 2 – 4 4 2 0 – 2 – 4
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6
2 . 4 2 . 0
1 . 6 1 . 2
0 . 8 0 . 4
0 . 0 G r a p h 1
d / m m
G r a p h 2 d / m m
(i) State what is meant by a travelling wave.
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(1)
(ii) Use the graphs to determine the amplitude, wavelength, frequency and speed of the
Refraction of waves
(b) The diagram below shows plane wavefronts incident on a boundary between two media A
and B.
m e d i u m A m e d i u m B
The ratio is1.4.
A medium of
index refractive
B medium of
index refractive
The angle between an incident wavefront and the normal to the boundary is 50.
(i) Calculate the angle between a refracted wavefront and the normal to the boundary.
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(3)
(ii) On the diagram above, construct three wavefronts to show the refraction of the
wave at the boundary.
(3)
Interference of waves
(c) State two conditions necessary to produce observable interference between light from two
sources.
1. ... 2. ...
(d) A Young’s double slit experiment for red light is set up as shown below.
s o u r c e o f w h i t e l i g h t
r e d f i l t e r d o u b l e s l i t
s i n g l e s l i t
s c r e e n
( n o t t o s c a l e )
An interference pattern of light and dark fringes is observed on the screen.
(i) The red filter is now replaced by a blue filter. State and explain the change in
appearance, other than change of colour, of the fringes on the screen. ... ... ...
(2)
(ii) The filter in (i) is removed. State and explain the appearance of the central
maximum fringe and also of fringes that are away from this central position. ... ... ... ... ...
Particle nature of light
(e) The photo-electric effect cannot be explained on the basis of a wave theory of
electromagnetic radiation. State two experimental observations, other than the existence of a threshold frequency, that led to this conclusion.
1. ... ... 2. ... ...
(2)
(f) Monochromatic light is incident on a metal surface in a photo-cell as shown below.
μA
m o n o c h r o m a t i c l i g h t
The metal surface has work function 2.4 eV and the threshold wavelength for light
incident on the surface is S. The current in the photo-cell is measured using a
microammeter.
Calculate the threshold wavelength S.
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(g) Light of wavelength 21
λ
S and intensity I is incident on the metal surface in (f). (Intensityis the light power incident per unit area.) The current in the photo-cell is iP.
State and explain the effect on the current iP in the photo-cell for light incident on the
surface
(i) of wavelength 12
λ
Sand intensity 2I;... ... ...
(3)
(ii) of wavelength less than 21
λ
Sand intensity I.... ... ...
3. X-ray spectra
The graph shows the variation with wavelength of the relative intensity of an X-ray spectrum
produced when electrons strike a metal target.
r e l a t i v e i n t e n s i t y
1 2 0 1 0 0
8 0 6 0
4 0 2 0
0
/ n m
The spectrum consists of a continuous spectrum and a line spectrum (the “spikes”).
(a) (i) State why there is a sharp cut-off at the short-wavelength end of the spectrum.
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(1)
(ii) Explain why the wavelengths of the line spectrum are characteristic of the target
element.
... ... ... ... ...
(b) In 1913, Moseley discovered that the frequency f of a line in the spectrum is related to the proton number (atomic number) Z of the target atoms by the expression
f = a(Z − b)2, where a and b are constants.
One line in the spectrum produced by a certain metal target has a wavelength of 0.154 nm.
For this line, a = 2.50 1015 Hz and b = 1.00.
Calculate the proton number of the target metal.
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(3)
(c) Determine the minimum potential difference through which electrons in the X-ray tube
must be accelerated so that the line of wavelength 0.154 nm may be observed in the spectrum.
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4. This question is about diffraction.
Plane wavefronts of monochromatic light of wavelength are incident on a rectangular slit of
width b. After passing through the slit, the light is brought to a focus on a screen distance D from the slit as shown below. The width of the slit is comparable to the wavelength of the incident
light and b D. The point P on the screen is opposite the centre of the slit.
P
s c r e e n s l i t
D b
The sketch graph below shows that the variation with angle
of the intensity of the light on thescreen.
i n t e n s i t y
(a) Explain qualitatively, this intensity distribution.
... ... ... ... ...
(3)
(b) The angle
=
is the angular half-width of the central maximum of the intensitydistribution and is given by the expression
= .b λ
Derive an expression in terms of D,
and b for the half-width d of the central maximum.
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(2)
(c) The single slit is replaced by two rectangular slits of width b. The distance between the
centre of the slits is equal to 2b.
On the axes below, draw a sketch of the intensity distribution on the screen. (The intensity distribution of a single slit is shown by the dotted line.)
i n t e n s i t y
