1. This question is about single slit diffraction.
The diagram below shows an experimental arrangement for observing Fraunhofer diffraction by
a single slit. After passing through the convex lens L1, monochromatic light from a point source
P is incident on a narrow, rectangular single slit. After passing through the slit the light is
brought to a focus on the screen by the lens L2. The point source P is at the focal point of the
lens L1.
s i n g l e s l i t
L L
s c r e e n
1 2
X P
The point X on the screen is directly opposite the central point of the slit.
(a) Explain qualitatively how Huygens’ principle accounts for the phenomenon of single slit
diffraction.
... ... ... ...
(b) Using the axes below draw a graph to show how the intensity of the pattern varies with
distance along the screen. The point X on the screen is shown as a reference point. (This is
a sketch graph; you do not need to add any numerical values.)
(3)
i n t e n s i t y
d i s t a n c e a l o n g s c r e e n X
(c) In this experiment the light has a wavelength of 500 nm and the width of the central
maximum of intensity on the screen is 10.0 mm. When light of unknown wavelength λ is used, the width of the central maximum of intensity is 13.0 mm. Determine the value of λ. ... ... ... ...
(2)
The lens L1 is now removed and another point source Q emitting light of the same wavelength as
P (500 nm) is placed 5.0 mm from P and the two sources are arranged as shown below.
1 . 5 0 m 5 . 0 m m
P
Q
(d) (i) State the condition for the image of P and the image of Q formed on the screen to be just resolved.
... ...
(1)
(ii) Determine the minimum width b of the slit for the two images to be just resolved.
... ... ... ... ...
(2) (Total 10 marks)
2. This question is about the formation of coloured fringes when white light is reflected from thin
films.
(a) Name the wave phenomenon that is responsible for the formation of regions of different
colour when white light is reflected from a thin film of oil floating on water. ... ...
(1)
(b) A film of oil of refractive index 1.45 floats on a layer of water of refractive index 1.33 and
is illuminated by white light at normal incidence.
I l l u m i n a t i o n A i r
When viewed at near normal incidence a particular region of the film looks red, with an average
wavelength of about 650 nm. An equation relating this dominant average wavelength λ, to the
minimum film thickness of the region t, is λ = 4nt.
(i) State what property n measures and explain why it enters into the equation.
... ... ... ...
(2)
(ii) Calculate the minimum film thickness.
... ... ...
(1)
(iii) Describe the change to the conditions for reflection that would result if the oil film was spread over a flat sheet of glass of refractive index 1.76, rather than floating on water.
... ... ... ...
(2) (Total 6 marks)
3. This question is about resolution.
(a) State the name of the wave phenomenon that limits the resolution of any optical
instrument.
... ...
(b) Explain with the aid of a diagram, the Rayleigh criterion.
... ... ... ...
(3) (Total 4 marks)
4. This question is about optical resolution.
(a) Light from a point source is brought to a focus by a convex lens. The lens does not cause
spherical or chromatic aberration.
(i) State why the image of the point source will not be a point image.
... ...
(1)
(ii) Describe the appearance of the image.
... ... ... ...
Two light receptors at the back of the eye are 4.0 μm apart. The distance of the receptors from the convex lens at the front of the eye is 17.0 mm, as shown below.
1 7 . 0 m m e y e l e n s
l i g h t r e c e p t o r
4 . 0 m
Light of wavelength 550 nm from two point objects enters the eye. The centres of the images of the two objects are focused on the light receptors.
(b) (i) Calculate the angle α in radians subtended by the two receptors at the centre of the
eye lens.
... ... ... ...
(2)
(ii) Use the Rayleigh criterion to calculate the diameter of the pupil of the eye so that
the two images are just resolved.
... ...
5. This question is about oil films.
Explain briefly the formation of coloured images when white light is reflected at a film of oil on water.
... ... ... ... ... ... ...
(Total 3 marks)
6. This question is about thin film interference.
Two flat glass plates are in contact along one edge and are separated by a piece of thin metal foil placed parallel to the edge, as shown below.
D i a g r a m n o t d r a w n t o s c a l e
m e t a l f o i l l i g h t o f w a v e l e n g t h
5 . 8 9 1 0 mx
g l a s s p l a t e
l i n e o f c o n t a c t
– 7
Air is trapped between the two plates. The gap between the two plates is viewed normally using
reflected light of wavelength 5.89 × 10–7 m.
A series of straight fringes, parallel to the line of contact of the plates is seen.
(a) State what can be deduced from the fact that the fringes are straight and parallel.
...
(b) Explain why a dark fringe is observed along the line of contact of the glass plates. ... ... ... ...
(3)
(c) The distance between the line of contact of the plates and the edge of the metal foil is
9.0 cm. The dark fringes are each separated by a distance of 1.4 mm. Calculate the thickness of the metal foil.
... ... ... ...
(3)
The lenses used in astronomical telescopes are frequently “bloomed”. This means that a thin film is deposited on the lens in order to reduce the intensity of unwanted light reflected by the lens. Destructive interference occurs between the light reflected from the upper and the lower surfaces of the film. The reflections at both surfaces for one incident ray are shown in the diagram.
a i r
f i l m
g l a s s
(d) (i) State why complete destructive interference of all the reflected light does not occur.
... ...
(ii) With reference to your answer in (i), suggest why the film appears to be coloured. ... ... ...
(2) (Total 10 marks)
7. A student uses a diffraction grating to view the visible part of the sodium emission spectrum.
(a) Explain how the diffraction grating is able to separate light into component wavelengths.
... ... ...
(3)
(b) Sodium light is incident normally on a grating having 6000 lines per centimetre. Calculate
the angle at which light of wavelength 589.6 nm will be seen in the first order spectrum. ... ... ...
8. 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 × 10–4 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.
... ... ...
9. This question is about diffraction at a single slit.
Plane wavefronts of monochromatic light are incident on a narrow, rectangular slit whose width
b is comparable to the wavelength λ of the light. After passing through the slit, the light is
brought to a focus on a screen.
Z W
X b
Q
Y
P
s l i t s c r e e n
The line XY, normal to the plane of the slit, is drawn from the centre of the slit to the screen and
the pointsPandQare the first points of minimum intensity as measured from point Y.
The diagram also shows two rays of light incident on the screen at point P. Ray ZP leaves one edge of the slit and ray XP leaves the centre of the slit.
The angle
is small.(a) On the diagram, label the half angular width θ of the central maximum of the diffraction
pattern.
(1)
(b) State and explain an expression, in terms of λ for the path difference ZW between the rays
ZP and XP.
... ...
(c) Hence deduce that the half angular width θ is given by the expression
θ =
b λ
... ... ... ... ...
(3)
(d) In a particular demonstration of single slit diffraction, λ = 450 nm, b = 0.15 mm and the
screen is a long way from the slits.
Calculate the angular width of the central maximum of the diffraction pattern on the screen.
... ...
(2)
Using light of the same wavelength as above (450 nm), an arrangement is set up to demonstrate diffraction by a double slit. Each slit has the same width as that above (0.15 mm) and the slit
separation is d. The graph below shows the variation with the angle of diffraction ψ of the
intensity I of the diffraction pattern on the screen.
– 1 0 – 5 0 5 / × 1 0 r a d 1 0
I / a r b i t r a r y u n i t s
– 3
(e) Calculate the slit separation d.
... ... ... ...
(2) (Total 10 marks)
10. 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.
s l i t
s c r e e n A
B
l i g h t s o u r c e s
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)
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)
The bright star Sirius A is accompanied by a much fainter star, Sirius B. The mean distance of
the stars from Earth is 8.1 × 1016 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) (Total 6 marks)
11. Monochromatic parallel light is incident on two slits of equal width and close together. After
passing through the slits, the light is brought to a focus on a screen. The diagram below shows the intensity distribution of the light on the screen.
I
d i s t a n c e a l o n g t h e s c r e e n
A B
(a) Light from the same source is incident on many slits of the same width as the widths of
the slits above. Draw on the above diagram, a possible new intensity distribution of the light on the screen between the points A and B on the screen.
A parallel beam of light of wavelength 450 nm is incident at right angles on a diffraction grating.
The slit spacing of the diffraction grating is 1.25 × 10–6 m.
(b) Determine the angle between the central maximum and first order principal maximum
formed by the grating.
... ... ... ...
(2) (Total 4 marks)
12. This question is about thin film interference.
Monochromatic light is incident on a thin film of transparent plastic as shown below.
C
m o n o c h r o m a t i c A B
l i g h t
f i l m
The plastic film is in air.
Light is partially reflected at both surface A and surface B of the film.
(a) State the phase change that occurs when light is reflected from
(i) surface A;
...
(1)
The light incident on the plastic has a wavelength of 620 nm. The refractive index of the plastic is 1.4.
(b) Calculate the minimum thickness of the film for the light reflected from surface A and
surface B to undergo destructive interference.
... ... ... ...
(3) (Total 5 marks)
13. This question is about two-source interference.
A double slit is illuminated normally with coherent light. The interference pattern is observed on a screen. The apparatus is shown below.
n o t t o s c a l e
c o h e r e n t l i g h t s
s c r e e n
The width of both slits in the double slit arrangement is increased without altering the separation s.
Describe and explain the effect, if any, of this change on
(a) the number of fringes observed;
... ... ...
(b) the intensity of the fringes.
... ... ... ...
(3) (Total 5 marks)
14. This question is about thin film interference.
A thin film of colourless oil floats on water. Light is reflected from the upper and the lower surfaces of the film as shown below.
o b s e r v e r
r a y A r a y B
a i r
o i l d
w a t e r
The refractive index for light in the oil is greater than the refractive index for light in the air. The refractive index for light in the oil is less than the refractive index for light in the water.
The light has wavelength in the oil.
(a) State, in terms of , a value for the thickness d that causes rays A and B to interfere
(b) White light is now incident on the oil film. Explain why, for one thickness d of the oil film, the film appears to have a purple (magenta) colour.
... ... ...
15. This question is about a wedge film.
A lensmaker will sometimes check the shape of a lens surface by resting the lens on a flat sheet of glass and then viewing the arrangement in monochromatic light at near-normal incidence, as shown in the diagram below.
l i g h t s o u r c e
l e n s
g l a s s s h e e t
This produces a circular interference pattern with a dark centre, as shown below.
b r i g h t f r i n g e s
16. This question is about a wedge film.
In an experiment to measure the thickness d of a piece of adhesive tape, the tape is used to
separate two flat plates of glass as shown below. This forms a wedge shaped air film.
m i c r o s c o p i c
h a l f – s i l v e r e d m i r r o r m o n o c h r o m a t i c l i g h t 4 8 0 n m
g l a s s p l a t e d
a d h e s i v e t a p e
5 . 0 1 0 – 2
m
g l a s s p l a t eA beam of monochromatic light is incident on the wedge film. The light that is reflected at right angles to the wedge, is viewed using the microscope. A system of parallel fringes of equal spacing is observed in the field of view of the microscope.
(a) Outline how the fringe system is formed.
... ... ... ...
(2)
(b) The spacing between the fringes is 1.2 10–4 m. The distance from where the two plates
of glass touch and the edge of the adhesive tape is 5.0 10–2 m. The wavelength of the
light is 480 nm. Estimate the thickness d of the adhesive tape.
... ... ... ... ...
17. This question is about a diffraction grating.
Light of wavelength 590 nm is incident normally on a diffraction grating, as shown below.
f i r s t o r d e r
z e r o o r d e r
f i r s t o r d e r l i g h t w a v e l e n g t h
5 9 0 n m
g r a t i n g
6 . 0 1 0 l i n e s p e r m e t r e5
The grating has 6.0 105 lines per metre.
(a) Determine the total number of orders of diffracted light, including the zero order, that can
be observed.
... ... ... ... ...
(4)
(b) The incident light is replaced by a beam of light consisting of two wavelengths, 590 nm
and 589 nm.
State two observable differences between a first order spectrum and a second order spectrum of the diffracted light.
1. ... ... 2. ... ...
18. This question is about thin films.
A thin film of oil is floating on some water. White light is reflected from the oil film. A series of coloured fringes is seen.
(a) State the name of the wave phenomenon that gives rise to the formation of the coloured
fringes.
...
(1)
(b) Describe why the oil film appears to change colour when viewed from different angles of
incidence.
... ... ... ...
(3) (Total 4 marks)
19. 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) In the space provided below, draw a labelled sketch to show the diffraction fringe
pattern produced on the photographic plate.
(ii) Calculate the diameter of the central maximum on the photographic plate. ... ... ... ... ... ...
(2)
(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.
... ... ... ... ... ... ... ...
(ii) Over a period of time the separation of the stars varies from
2
d
to 2d.
Describe and explain the changes to the image produced by the telescope during this time. You should include diagrams to illustrate your answer.
... ... ... ... ... ... ...
(3) (Total 10 marks)
20. This question is about diffraction.
Monochromatic light is incident on a single slit of width 1.2×10–4 m.
i n c i d e n t l i g h t
1 . 2 1 0 m× – 4
D i a g r a m n o t t o s c a l e
The graph shows the variation with angle
of the intensity of the light on the screen.r e l a t i v e i n t e n s i t y
/ × 1 0 – 3r a d
1
0 . 8
0 . 6
0 . 4
0 . 2
0 . 0
– 6 – 4 – 2 0 2 4 6 θ
(a) Use the graph to estimate the wavelength of the light.
... ...
(1)
(b) Monochromatic light is incident on two parallel slits. After passing through the slits, the
light is incident on a screen. The separation of the slits is approximately twice the slit width. On the axes above draw a graph to show the intensity distribution of the light on the screen.
21. This question is about thin film interference.
The diagram shows monochromatic light in air, that is incident on a thin film of silicon oxide of
thickness d.
i n c i d e n t r a y
n o r m a l A B
a i r
s i l i c o n o x i d e
a i r
d θ
The light is incident at an angle
to the normal to the surface. Light is reflected along directionsA and B.
(a) State why light waves along A and B are coherent.
...
(1)
(b) The wavelength of the light in the silicon oxide film is 452 nm. The light is incident
normally on the surface so that
= 0. Calculate the minimum thickness of the film suchthat light along A and B undergoes destructive interference.
... ... ... ... ...
(4)
(c) The light incident on the film is replaced by white light. State and explain the appearance
of the film in this case.
...
22. This question is about single-slit diffraction.
(a) Explain, by reference to secondary wavelets, the diffraction of light at a single slit.
... ... ... ...
(2)
(b) Light from a helium-neon laser passes through a narrow slit and is incident on a screen 2.4
m distance from the slit. The graph below shows the variation with intensity I of the light
on the screen of distance x along the screen.
I
– 1 0 – 5 0 5 1 0
x / m m
(i) The wavelength of the light emitted by the laser is 630 nm. Use data from the graph
above to determine the width of the slit.
... ... ... ... ...
(ii) State two changes to the intensity distribution of the central maximum when the single slit is replaced by one of greater width.
1. ... 2. ...
(2) (Total 7 marks)
23. This question is about thin film interference.
Outline the reason why, when white light is reflected from the surface of an oil film, a system of coloured fringes is observed.
... ... ... ... ...
24. This question is about interference and diffraction.
Light from a laser is incident on two slits of equal width. After passing through the slits, the light is incident on a screen. The diagram below shows the intensity distribution of the light on the screen.
(a) The wavelength of the light from the laser is 633 nm and the angular separation of the
bright fringes on the screen is 4.00 10–4 rad. Calculate the separation of the slits.
... ... ... ... ...
(3)
(b) Light from the laser is incident on many slits of the same width as the widths of the slits
above. Draw, on the above diagram, a possible new intensity distribution of the light on the screen.
(2)
(c) The laser is replaced by a source of white light. Describe, if any, the changes to the fringes
on the screen.
25. This question is about a wedge film.
In an experiment to measure the thickness d of a piece of adhesive tape, the tape is used to
separate two flat plates of glass as shown below. This forms a wedge shaped air film.
A beam of monochromatic light is incident on the wedge film. The light that is reflected at right angles to the wedge, is viewed using the microscope. A system of parallel fringes of equal spacing is observed in the field of view of the microscope.
(a) Outline how the fringe system is formed.
... ... ... ...
(2)
(b) The spacing between the fringes is 1.2 10–4 m. The distance from where the two plates
of glass touch and the edge of the adhesive tape is 5.0 10–2 m. The wavelength of the
light is 480 nm. Estimate the thickness d of the adhesive tape.
... ... ... ... ...
