Q1.
(a)
A laser emits monochromatic light.
Explain the meaning of the term monochromatic light.
........................................................................................................................
........................................................................................................................
(1)
(b)
The diagram below shows a laser emitting blue light directed at a single slit, where the slit
width is greater than the wavelength of the light. The intensity graph for the diffracted blue
light is shown.
The laser is replaced by a laser emitting red light.
On the axes shown in the diagram above sketch the intensity graph for a laser emitting red
light.
(2)
Page 1 of 33
(c)
State and explain one precaution that should be taken when using laser light
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(d)
The red laser light is replaced by a non-laser source emitting white light.
Describe how the appearance of the pattern would change.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 8 marks)
Page 2 of 33
Q2.
The diagram below shows the paths of microwaves from two narrow slits, acting as
coherent sources, through a vacuum to a detector.
(a)
Explain what is meant by coherent sources.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(b)
(i)
The frequency of the microwaves is 9.4 GHz.
Calculate the wavelength of the waves.
wavelength = ................................. m
(2)
Page 3 of 33
(ii)
Using the diagram above and your answer to part (b)(i), calculate the path difference
between the two waves arriving at the detector.
path difference = ................................. m
(1)
(c)
State and explain whether a maximum or minimum is detected at the position shown in the
diagram above.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(d)
The experiment is now rearranged so that the perpendicular distance from the slits to the
detector is 0.42 m. The interference fringe spacing changes to 0.11 m.
Calculate the slit separation. Give your answer to an appropriate number of significant
figures.
slit separation = ................................. m
(3)
(e)
With the detector at the position of a maximum, the frequency of the microwaves is now
doubled. State and explain what would now be detected by the detector in the same
position.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 14 marks)
Page 4 of 33
Q3.
(a) In an experiment, a narrow beam of white light from a filament lamp is directed at
normal incidence at a diffraction grating. Complete the diagram in the figure below to show
the light beams transmitted by the grating, showing the zero-order beam and the first-order
beams.
(3)
(b)
Light from a star is passed through the grating.
Explain how the appearance of the first-order beam can be used to deduce one piece of
information about the gases that make up the outer layers of the star.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(c)
In an experiment, a laser is used with a diffraction grating of known number of lines per
mm to measure the wavelength of the laser light.
(i)
Draw a labelled diagram of a suitable arrangement to carry out this experiment.
(2)
Page 5 of 33
(ii)
Describe the necessary procedure in order to obtain an accurate and reliable value
for the wavelength of the laser light.
Your answer should include details of all the measurements and necessary
calculations.
The quality of your written communication will be assessed in your answer.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
(6)
(Total 13 marks)
Q4.
A single slit diffraction pattern is produced on a screen using a laser. The intensity of the
central maximum is plotted on the axes in the figure below.
(a)
On the figure above, sketch how the intensity varies across the screen to the right of the
central maximum.
(2)
Page 6 of 33
(b)
A laser is a source of monochromatic, coherent light. State what is meant by
monochromatic light ....................................................................................
......................................................................................................................
coherent light ...............................................................................................
......................................................................................................................
(2)
(c)
Describe how the pattern would change if light of a longer wavelength was used.
......................................................................................................................
......................................................................................................................
(1)
(d)
State two ways in which the appearance of the fringes would change if the slit was made
narrower.
......................................................................................................................
......................................................................................................................
(2)
(e)
The laser is replaced with a lamp that produces a narrow beam of white light. Sketch and
label the appearance of the fringes as you would see them on a screen.
(3)
(Total 10 marks)
Page 7 of 33
Q5.
For a plane transmission diffraction grating, the diffraction grating equation for the first order
beam is:
λ = d sin θ
(a)
The figure below shows two of the slits in the grating. Label the figure below with the
distances d and λ.
(2)
(b)
State and explain what happens to the value of angle θ for the first order beam if the
wavelength of the monochromatic light decreases.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
Page 8 of 33
(c)
A diffraction grating was used with a spectrometer to obtain the line spectrum of star X
shown in the figure below. Shown are some line spectra for six elements that have been
obtained in the laboratory.
Place ticks in the boxes next to the three elements that are present in the atmosphere of
star X.
(2)
(d)
The diffraction grating used to obtain the spectrum of star X had 300 slits per mm.
(i)
Calculate the distance between the centres of two adjacent slits on this grating.
answer = ................................. m
(1)
(ii)
Calculate the first order angle of diffraction of line P in the figure above.
answer = ........................ degrees
(2)
(Total 9 marks)
Page 9 of 33
Q6.
Just over two hundred years ago Thomas Young demonstrated the interference of light by
illuminating two closely spaced narrow slits with light from a single light source.
(a)
What did this suggest to Young about the nature of light?
......................................................................................................................
......................................................................................................................
(1)
(b)
The demonstration can be carried out more conveniently with a laser. A laser produces
coherent, monochromatic light.
(i)
State what is meant by monochromatic.
.............................................................................................................
.............................................................................................................
(ii)
State what is meant by coherent.
.............................................................................................................
.............................................................................................................
(2)
(iii)
State one safety precaution that should be taken while using a laser.
.............................................................................................................
.............................................................................................................
(1)
Page 10 of 33
(c)
The diagram below shows the maxima of a two slit interference pattern produced on a
screen when a laser was used as a monochromatic light source.
The slit spacing = 0.30 mm.
The distance from the slits to the screen = 10.0 m.
Use the diagram above to calculate the wavelength of the light that produced the pattern.
answer = ...................................... m
(3)
(d)
The laser is replaced by another laser emitting visible light with a shorter wavelength.
State and explain how this will affect the spacing of the maxima on the screen.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 9 marks)
Page 11 of 33
Q7.
A narrow beam of monochromatic light of wavelength 590 nm is directed normally at a
diffraction grating, as shown in the diagram below.
(a)
The grating spacing of the diffraction grating is 1.67 × 10–6 m.
(i)
Calculate the angle of diffraction of the second order diffracted beam.
answer .................................... degrees
(4)
(ii)
Show that no beams higher than the second order can be observed at this
wavelength.
(3)
(b)
The light source is replaced by a monochromatic light source of unknown wavelength.
A narrow beam of light from this light source is directed normally at the grating.
Measurement of the angle of diffraction of the second order beam gives a value of 42.1°.
Calculate the wavelength of this light source.
answer ....................................... m
(2)
(Total 9 marks)
Page 12 of 33
Q8.
A narrow beam of monochromatic red light is directed at a double slit arrangement. Parallel
red and dark fringes are seen on the screen shown in the diagram above.
(a)
(i)
Light passing through each slit spreads out. What is the name for this effect?
.............................................................................................................
(1)
(ii)
Explain the formation of the fringes seen on the screen.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(iii)
The slit spacing was 0.56 mm. The distance across 4 fringe spacings was 3.6 mm
when the screen was at a distance of 0.80 m from the slits. Calculate the
wavelength of the red light.
Answer ..................... m
(4)
Page 13 of 33
(b)
Describe how the appearance of the fringes would differ if white light had been used
instead of red light.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(Total 12 marks)
Q9.
(a)
State what is meant by coherent sources of light.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
Page 14 of 33
(b)
Figure 1
Young’s fringes are produced on the screen from the monochromatic source by the
arrangement shown in Figure 1.
You may be awarded marks for the quality of written communication in your answers.
(i)
Explain why slit S should be narrow.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
Why do slits S1 and S2 act as coherent sources?
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
Page 15 of 33
(c)
The pattern on the screen may be represented as a graph of intensity against position on
the screen. The central fringe is shown on the graph in Figure 2. Complete this graph to
represent the rest of the pattern by drawing on Figure 2.
Figure 2
(2)
(Total 8 marks)
Page 16 of 33
Q10.
A vertical screen is placed several metres beyond a vertical double slit arrangement
illuminated by a laser. The diagram below shows a full-size tracing of the pattern of spots
obtained on this screen. The black patches represent red light whilst the spaces between them
are dark.
(a)
Using the wave theory, explain how the pattern of bright and dark patches is formed.
You may be awarded marks for the quality of written communication provided in your
answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(b)
The slit separation was 0.90 mm and the distance between the slits and the screen was
4.2 m.
(i)
Calculate the spacing of the bright fringes by taking measurements on the diagram of
the tracing.
.............................................................................................................
.............................................................................................................
(ii)
Hence determine the wavelength of the laser light used.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(Total 7 marks)
Page 17 of 33
M1.
(a)
single frequency (or wavelength or photon energy)
not single colour
accept ‘very narrow band of frequencies’
1
(b)
subsidiary maxima (centre of) peaks further away from centre
For second mark: One square tolerance horizontally. One whole
subsid max seen on either side.
subsidiary maxima peaks further away from centre AND central maximum twice width of
subsidiaries AND symmetrical
Central higher than subsid and subsid same height + / − 2
squares. Minima on the x axis + / − 1 square.
Must see 1 whole subsidiary for second mark
2
(c)
ONE FROM:
•
•
•
•
•
•
don't shine towards a person
avoid (accidental) reflections
wear laser safety goggles
'laser on' warning light outside room
Stand behind laser
other sensible suggestion
allow green goggles for red laser, ‘high intensity goggles’, etc.
not ‘goggles’, ‘sunglasses’
eye / skin damage could occur
2
(d)
3 from 4
•
•
•
•
central white (fringe)
each / every / all subsidiary maxima are composed of a spectrum (clearly stated or
implied)
each / every / all subsidiary maxima are composed of a spectrum (clearly stated or
implied) AND (subsidiary maxima) have violet (allow blue) nearest central maximum
OR red furthest from centre
Fringe spacing less / maxima are wider / dark fringes are smaller (or not present)
allow ‘white in middle’
For second mark do not allow ‘there are colours’ or ‘there is a
spectrum’ on their own
Allow ‘rainbow pattern’ instead of spectrum but not ‘a rainbow’
Allow ‘rainbow pattern’ instead of spectrum but not ‘a rainbow’
If they get the first, the second and third are easier to award
Allow full credit for annotated sketch
3
[8]
M2.
(a)
same wavelength / frequency
constant phase relationship
allow ‘constant phase difference’ but not ‘in phase’
2
Page 18 of 33
(b)
(λ=
(i)
)
Use of speed of sound gets zero
3.00 × 108 = 9.4 (109) λ
OR
= 3.2 × 10−2 (3.19 × 10−2 m)
Allow 0.03
2
(ii)
3.2 × 10−2
(m) ecf from bi
Don’t allow ‘1 wavelength’, 1λ, etc
Do not accept: zero, 2 , 360 °
1
(c)
maximum (at position shown)
allow constructive superposition.
‘Addition’ is not enough
constructive interference / reinforcement
ecf for ‘minimum’ or for reference to wrong maximum
(the waves meet) ‘in step’ / peak meets peak / trough meets trough / path difference is (n)
λ / in phase
3
(d)
s=
Don’t allow use of the diagram shown as a scale diagram
ecf bi
Do not penalise s and w symbols wrong way round in working if
answer is correct.
= 0.12 (0.1218 m)
Correct answer gains first two marks.
= any 2sf number
Independent sf mark for any 2 sf number
3
(e)
a maximum
Candidates stating ‘ minimum ’ can get second mark only
(f × 2 results in) λ/2
path difference is an even number of multiples of the new wavelength ( 2n λ new )
allow ‘path difference is nλ’ / any even number of multiples of the new λ quoted e.g. ‘path
difference is now 2 λ’
3
[14]
Page 19 of 33
M3.
(a)
max three from
central maximum shown
two equally spaced first order maxima
central and one first order labelled correctly
central white maximum
indication of spectra/colours in at least one first order beam
at least one first order beam labelled with violet (indigo or blue) closest to the
centre or red furthest
3
(b)
dark/black lines or absorption spectrum or Fraunhofer lines
(reveal the) composition (of the star’s atmosphere)
accept dark ‘bands’
accept atoms or elements in the star
or the peak of intensity
(is related to) the temperature
or Doppler (blue or red) shift
(speed of) rotation or speed of star (relative to Earth)
2
(c)
(i)
grating and screen shown with both labelled
laser or laser beam labelled
2
(ii)
The candidate’s writing should be legible and the spelling, punctuation
and grammar should be sufficiently accurate for the meaning to be clear.
The candidate’s answer will be assessed holistically. The answer will be
assigned to one of three levels according to the following criteria.
Page 20 of 33
High Level (Good to excellent): 5 or 6 marks
The information conveyed by the answer is clearly organised, logical and
coherent, using appropriate specialist vocabulary correctly. The form and style
of writing is appropriate to answer the question.
•
correct use of (n)λ = d sin θ
•
and measure appropriate angle (eg ‘to first order beam’ is the minimum
required)
•
and method to measure angle (eg tan θ = x/D, spectrometer, accept
protractor)
•
and at least one way of improving accuracy/reliability
•
for full marks: also explain how d is calculated, eg d = 1/ lines per mm
(× 103)
Intermediate Level (Modest to adequate): 3 or 4 marks
The information conveyed by the answer may be less well organised and not
fully coherent. There is less use of specialist vocabulary, or specialist
vocabulary may be used incorrectly. The form and style of writing is less
appropriate.
•
use of (n)λ = d sin θ
•
and measure appropriate angle (eg ‘to first order beam’ is the minimum
required)
•
and method of measurement of θ (eg tan θ = x/D, spectrometer, accept
protractor) or at least one way of improving accuracy/reliability
Low Level (Poor to limited): 1 or 2 marks
The information conveyed by the answer is poorly organised and may not be
relevant or coherent. There is little correct use of specialist vocabulary. The form
and style of writing may be only partly appropriate.
•
use of (n)λ = d sin θ
•
or measure appropriate angle (eg ‘to first order beam’ is the minimum
required)
•
or at least one way of improving accuracy/reliability
Incorrect, inappropriate of no response: 0 marks
No answer or answer refers to unrelated, incorrect or inappropriate physics.
Page 21 of 33
The explanation expected in a competent answer should include
Accuracy/reliability points
•
measure between more than one order (eg 2 θ)
•
measure θ for different orders (for average λ not average angle)
•
check or repeat/repeat for different distances (D)
•
use of spectrometer
•
use large distance to screen (D)
•
protractor with 0.5 degree (or less) intervals
•
graphical method: plot sin θ against n (gradient = λ/d)
6
[13]
M4.
(a)
3 subsidiary maxima in correct positions (1)
intensity decreasing (1)
2
(b)
a single wavelength (1)
constant phase relationship/difference (1)
2
(c)
maxima further apart/central maximum wider/subsidiary maximum
wider/maxima are wider (1)
1
(d)
wider/increased separation (1)
lower intensity (1)
2
Page 22 of 33
(e)
distinct fringes shown with subsidiary maxima (1)
indication that colours are present within each subsidiary maxima (1)
blue/violet on the inner edge or red outer for at least one subsidiary
maximum (1)
(middle of) central maximum white (1)
3
[10]
M5.
(a)
λ correct (1)
d correct (1) arrow or line needed, both ends extending beyond
central black line
2
(b)
angle θ gets smaller (1)
because path difference gets smaller/d constant, (λ smaller) so
sin θ smaller (1)
max 1 for correct explanation for λ increasing
2
(c)
boxes 1,5,6 (1)(1)
two correct 1 mark
4 ticks max 1
5 or 6 ticks gets 0
2
(d)
(i)
3.3 × 10–6 m (1) (1/300 = 3.33 × 10–3 mm, 3300 nm) DNA 1 sf here
DNA 1/300 000 as answer
accept 3 1/3 × 10–6, 3.33 × 10–6 recurring, etc
1
(ii)
(sin θ =)
(1)
correct wavelength used and seen (545 to 548 × 10–9)
and 9.4 to 9.6 (°) (1) ecf (d) (i), for correct wavelength only
(545 to 548 × 10–9)
2
[9]
Page 23 of 33
M6.
(a) showed that light was a wave (rather than a particle)/wave nature
(of light) (1)
1
(b)
(i)
single wavelength (or frequency) (1)
1
(ii)
(waves/source(s) have) constant phase difference (1)
1
(iii)
any sensible precaution, eg do not look into laser/do not point
the laser at others/do not let (regular) reflections enter the
eye/safety signs/suitable safety goggles (1)
1
(c)
(0.16/8) = 0.02(0) (1)
=
(1) ecf from calculation of fringe spacing
= 6.0 × 10–7 m (1) (= 600 nm) ecf from calculation of fringe spacing
3
(d)
maxima closer together (1)
(quotes equation and states that) spacing is proportional to wavelength/
D and s are constant therefore as λ decreases so ω decreases (1)
or links smaller wavelength to smaller path difference (1)
2
[9]
M7.
(a)
(i)
= 590 × 10–9m (1)
(using d sin θ = nλ gives)
(1) = 0.707 or
7.07 × 108 if nm used (1)
θ = 45.0° (1) (accept 45°)
Page 24 of 33
(ii)
(sin θ ≤ 1) gives
≤ 1 or n ≤ or =
(1) = 2.83 (1)
so 3rd order or higher order is not possible (1)
alternative solution:
(substituting) n = 3 (into d sin θ = nλ gives) (1)
sin θ (
) = 1.06 (1)
gives ‘error’/which is not possible (1)
7
(b)
(using d sin θ = nλ gives)
2 λ = 1.67 × 10–6 × sin 42.1 (1)
λ(= 0.5 × 1.67 × 10–6 × sin 42.1) = 5.6(0) × 10–7 m (or 560 nm) (1)
2
[9]
M8.
(a)
(ii)
(i)
diffraction (1)
any 4 points from
interference (fringes formed) (1)
where light from the two slits overlaps (or superposes) (1)
bright (or red) fringes are formed where light (from the two
slits) reinforces (or interfere constructively/crest meets crest) (1)
dark fringes are formed where light (from the two slits)
cancels (or interferes destructively/trough meets crest) (1)
the light (from the two slits) is coherent (1)
either
reinforcement occurs where light waves are in phase
(or path difference = whole number of wavelengths) (1)
or
cancellation occurs where light waves are out of phase of 180°
(in anti-phase)
(or path difference = whole number + 0.5 wavelengths) (1)
(not ‘out of phase’)
Page 25 of 33
gives λ =
(iii)
(1)
w (= 3.6/4) = 0.9(0) mm (1) (failure to /4 is max 2)
λ
(1) = 6.3 × 10–7 m (1)
9
(b)
central (bright) fringe would be white (1)
side fringes are (continuous) spectra (1)
(dark) fringes would be closer together (because λred > average λwhite) (1)
the bright fringes would be blue on the side nearest the centre
(or red on the side away from the centre) (1)
bright fringes merge away from centre (1)
bright fringes wider (or dark fringes narrower) (1)
max 3
[12]
M9.
(a) same wavelength or frequency (1)
(same phase or) constant phase difference (1)
2
(b)
(i)
narrow slit gives wide diffraction (1)
(to ensure that) both S1 and S2 are illuminated (1)
(ii)
slit S acts as a point source (1)
S1 and S2 are illuminated from same source giving
monochromatic/same λ (1)
paths to S1 and S2 are of constant length giving constant phase
difference (1)
[or SS1 = SS2 so waves are in phase]
Max 4
QWC 1
(c)
graph to show:
maxima of similar intensity to central maximum (1)
[or some decrease in intensity outwards from centre]
all fringes same width as central fringe (1)
2
[8]
Page 26 of 33
M10.
(a) slits act as coherent sources (1)
waves/light diffract at slits (1)
waves overlap/superpose/meet/cross (1)
bright patches : constructive/waves in phase/reinforce (1)
dark patches : destructive/waves out of phase/cancel (1)
max 3
QWC 2
(b)
(i)
spacing w =
= 3.0 or 2.9 mm (1) (2.92 ± 0.04 mm)
15 or more fringes used (1)
(ii)
(use of λ =
gives)
λ=
(1)
= 6.26 × 10-7
(allow C.E. for sensible value of w from (i))
4
[7]
Page 27 of 33
E1.
(a) In general, this was a well answered question apart from a tendency for candidates to
add extra detail, e.g. ‘single wavelength and coherent’; this loses the mark. As does: ‘single
wavelength / colour’; because this implies that monochromatic could be just a single
colour. However, ‘light of a single wavelength and therefore a single colour’ would be
acceptable. It is therefore best to learn the appropriate definition and not add any further
detail.
(b)
Many candidates did not know what to do on this question.
The red light subsidiary maxima were often shown closer to the central maximum than the
blue.
Perhaps single slit diffraction tends to be a little overlooked because the specification does
not require any mathematical description. Nevertheless, students should be shown
images of the single slit pattern and how it changes for different wavelengths. Images are
readily available on the internet via any search engine.
(c)
When talking about laser safety, it is not acceptable to say simply ‘wear goggles’. One
must say ‘laser safety goggles’, ‘laser safety glasses’, or ‘laser safety eyewear’. Standard
laboratory goggles would not afford any significant protection against laser light.
(d)
Only a few candidates were able to describe the pattern accurately. Answers tended to be
vague and ambiguous. Only a small number decided to add a sketch to clarify their
answer and this approach should be encouraged. Again, perhaps the single slit has been
overlooked by some in favour of the ‘more difficult’ double slit and grating.
E2.
(a) The explanation of coherent should include ‘constant phase relationship’ and ‘same
frequency’. Many only picked up one mark for stating one of these. Many said that the
waves were ‘in phase’ which was not enough for the mark.
(b)
(c)
(i)
Some did not realise that the speed of light was given on the data sheet. There were
many mistakes with the powers of ten; ‘M’ was often interpreted as 106 , 1012 or even
1015.
(ii)
Many did not attempt this. Some may have run out of time but many did not
understand the concept of path difference.
Some felt that although the waves arrived in phase, the point where they meet is ‘zero
displacement’ for both of them and therefore gives a zero reading.
Nodes and antinodes were often referred to as the peaks / troughs and points of zero
displacement on a progressive wave, e.g. two troughs meet to give destructive
interference. Nodes and antinodes were often mixed up – ‘anti’ wrongly associated with
‘minimum’ perhaps?
(d)
Quite a few did not express their answer to 2sf, believing that 3sf was appropriate or that 2
d.p. was required.
To help students remember to address the significant figure issue, one could advise them
to draw a line between the instruction: ‘...appropriate number of significant figures’ and the
answer line as soon as they read it in the question.
If the student is uncertain about which symbol represents slit separation and which
represents fringe spacing, they may still get the right answer and this was not penalised.
However, it is essential that s and D are not interchanged and this mistake led to many
candidates failing to access 2 of the marks.
Page 28 of 33
E3.
Part (a) was done well by most students. However, many would have benefitted from using a
protractor to get the angles between the zero order and the two first-order beams roughly equal.
In part (b), the basic requirement is that students know that dark lines (absorption lines) are seen
on the spectra from stars and that these reveal elements present in the outer layers of the star.
The mark scheme also credited other uses of a stars spectrum. Many students had the idea that
spectral lines revealed elements but few knew about absorption lines. This is an area where
students who have taken PHYA1 first may have an advantage since they have studied atomic
energy levels and may have seen absorption spectra.
Labelling a laser, diffraction grating and some sort of screen or suitable detector was all that was
required for the two marks in part (c) (i). Many students missed out the screen. Some had
double slits instead of a grating.
Part (c) (ii) was, in general, poorly answered. Many students did not seem to be familiar with this
practical and instead described a two-slit approach to measuring wavelength. Those who
seemed familiar with the procedure tended not to fully answer the question which asked for
details of all the measurements and necessary calculations. The candidate who leaves out
these details is unlikely to be able to score more than two marks out of six even if they have
given a reasonable general description of the experiment. For example, they must include details
of how the angle is to be measured eg by measuring the distance between the zero order and
the first-order beam (using a ruler) and the distance between the screen and the grating. They
must then use tan θ = O/A to calculate the angle. Where students knew which equation to use,
they tended to know insufficient detail to score more than a few marks. Of those students who
did describe the use of a grating, many did not know the meanings of the symbols in the
equation eg, d was often thought to be the distance between grating and screen and n, the
number of lines per mm or even the refractive index of air. Many described measuring the
grating spacing with micrometers or metre rules, forgetting that the question stated that the lines
per mm are known.
In short, many of the students who took this exam seemed poorly prepared for this type of
question. They were, in some cases, able to produce an answer from a past paper for a closely
related, but significantly different, question. Many seemed unaware of the style and quality of
answer expected.
Most answers were vague, the literacy level was generally poor and there was a lack of detail
regarding the measurements and what should be done with them. This is often the case in the
January examination, but it is possible to improve the necessary skills even in the short
preparation time available. A few structured lessons on answering this type of question can to be
incorporated into schemes of work, allowing students to be fully aware of the expectations.
E4.
Most candidates gained at least one mark in part (a) for showing that the intensity of peaks
reduced with distance from the centre. However, many did not recall the key difference between
the pattern for single and double slits – the single slit pattern has a central maximum which is
double the width of the subsidiary maxima.
There were many correct definitions of monochromatic and coherent in part (b). A few stated
‘same colour’ for monochromatic and ‘in phase’ for coherent. Neither of these were accepted.
In part (c), many candidates incorrectly used the equation for two slits to show that the maxima
were further apart. This was not penalised since an explanation was not asked for.
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Many candidates got part (d) the wrong way around, saying that the fringes would be more
closely spaced and more intense. There seemed to be some guess work evident here.
Candidates need to be able to describe the appearance of the single slit pattern and be aware of
how it will change for different wavelengths, slit widths and for monochromatic and white light.
Some teachers introduce the equation for the single slit although it is not in the specification.
This is not necessary but can certainly help the more mathematically minded students. To
illustrate the change in the pattern, a simple demonstration can be carried out with a red and a
green laser shone through the same slit onto a screen.
A pleasing number of candidates produced very detailed and high quality answers to part (e),
with many gaining all three marks. Some drew a graph of intensity, which did not gain a mark on
its own.
E5.
Many candidates did not seem at all familiar with the use of this diagram in the derivation of
the grating equation in part (a) and the placing of the labels was often completely random. A
large number did not attempt to label the diagram and half of all candidates did not score any
marks.
Many who scored one mark had labelled the wavelength correctly but did not accurately indicate
the ‘line spacing’ with a suitable arrow or line.
Most candidates gained the first mark in part (b) for realising that sin θ decreased so θ would
decrease. Many candidates failed to gain the second mark by not stating that d remained
constant. Very few candidates attempted to explain in terms of path difference.
The majority of candidates had no problem matching up the spectral lines in part (c).
In part (d) (i), about half of all candidates were unable to convert lines per mm to line spacing
and there was considerable confusion with powers of ten. Many candidates did not convert to
metres and many also rounded to one significant figure.
In part (d) (ii) it was expected that the candidate would read an accurate value off the scale.
However, many chose a value to the nearest 10 nm, typically 550 nm. In this situation, it is
always best to interpolate when reading off the scale. The uncertainty in this reading can then be
expressed by giving the final answer to two significant figures. Line P is somewhere between
545 and 548 nm.
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E6.
Part (b) (i) was the definition of monochromatic. Most had no problem with this but a
significant number simply said ‘one colour’ and this was not enough.
In part (b) (ii) ‘constant phase relationship’ or ‘difference’ was expected but many candidates
said ‘in phase’ which was not given credit.
80% picked up the mark for a sensible suggestion in part (b) (iii) such as ‘never point the laser at
someone’. The other 20% suggested ‘goggles’, ‘safety goggles’, ‘tinted goggles’ which was not
enough. A few candidates said ‘specialised goggles’ or ‘goggles designed for use with lasers’
which was given credit.
Part (c) was a calculation using the two slit formula. 35% scored full marks. Common errors
included converting 0.30 mm to 3 × 10–3 m, using 0.16 as w, or using w = 0.16/9 rather than
0.16/8 due to counting dots rather than gaps and incorrectly rearranging the formula.
In part (d), the majority of candidates scored the first mark but were unable to explain why in a
convincing manner.
E7.
There were common mistakes to part (a) (i), such as failing to put n = 2. Some candidates
thought n was the refractive index and for this reason put n = 1. A significant number did not
convert from nm to m. Part (a) (ii) was done very well by the majority of candidates, either by
substituting in 90° or n = 3. Most were successful in finding the wavelength to part (b).
E8.
Part (a) (ii) was answered well by many who knew the terminology very well; most gained
three or four marks. The majority of the candidates who did not gain any marks had
misinterpreted the words ‘describe the formation’ to mean ‘describe the appearance’ rather than
‘how and why are they formed’.
Most candidates correctly rearranged the double slit formula in (a) (iii). It was then surprising that
very few candidates realised they had to divide 3.6 by 4 to get the fringe spacing and this limited
them to a maximum of two marks. Again many candidates who understood how to answer the
question then failed to get to grips with the powers of ten and dropped marks.
Most candidates did not gain any marks in part (b) and only very few gained full marks. Part of
the problem was that many believed that a single continuous spectrum would appear or that
each fringe would be a different colour. A useful exercise to overcome candidate’s difficulties
with descriptive answers could be to show interference phenomena and ask students to write a
detailed description as they are observing the pattern.
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E9.
Whilst it was generally recognised in part (a) that coherent sources provide waves of the
same wavelength (or frequency), the requirement about phase was less well understood. The
common answer was that the waves must be ‘in phase’, whilst the accepted answer was that
there has to be a constant phase relation between them. Although monochromatic sources that
are in phase will be coherent, coherence does not require the sources to be in phase. In part (b),
the single monochromatic source is the reason for fulfilling the same A criterion; this was
correctly quoted by most. Satisfactory explanations of how the phase criterion is satisfied were
very rare indeed, with few references to the paths SS1 and SS2.
Had part (c) required candidates to sketch Young’s fringes, there can be no doubt that the
responses would have been much more rewarding. Most candidates were unable to translate
their knowledge of the appearance of a familiar phenomenon into the required intensity/position
graph. Near the centre of the pattern, the fringes are all of very similar intensity and all should
have been drawn with the same width as the central fringe. The majority of wrong answers
showed either the single slit diffraction pattern, or fringes having the same width as the central
one but with much lower intensity.
E10.
Although some candidates thought part (a) was about the diffraction grating, the majority
gave good explanations of the double slit interference pattern. However, limitations over the use
of English caused difficulty in some scripts, where it was the laser that was passed through the
double slit system! Examiners were expecting to see references to waves diffracting from the
two coherent sources provided by the slits, then overlapping to produce constructive and
destructive interference effects on the screen. ‘Destructive’ sometimes became
‘deconstructive’, and there were frequent incorrect references to a phase difference of nλ.
Another common misunderstanding was that two troughs combine to give minimum
displacement.
An alarming lack of experimental knowledge and measurement technique became apparent in
the responses to part (b)(i). Large numbers of candidates were prepared only to give a bald
answer of 3 mm, with no explanation given. This received a significant figure penalty and both
marks for this part were lost. It was expected that the fringe spacing would be obtained from a
measurement taken over a large proportion of the fringe diagram and the result expressed to at
least two significant figures: 2.9 mm or 3.0 mm would have been acceptable. Even more
worrying were the candidates who showed complete misunderstanding of fringe spacing by
giving it as 1 mm, usually interpreted as the distance between the outer edges of two adjacent
black blobs in the diagram! Incorrect values of fringe spacing were treated as consequential
errors for part (b)(ii), therefore leaving both remaining marks accessible, unless the value for w
was badly wrong.
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