1. (i) when
(two) waves meet/combine/interact/superpose, etc. (at a point)
M1
there is a change in overall
intensity/displacement
allow
for A1 mark: (vector) sum/resultant displacement(s)/AW
A1
(ii) constant
phase difference/relationship (between the waves)
just
stating same frequency not sufficient
B1
[3]
2. (i) path difference of nλ for
constructive interference
allow
waves arrive in phase
M1
producing either maximum
amplitude/intensity or a maximum
A1
path difference of (2n + 1)λ/2
for destructive interference
allow
waves arrive in anti-/out of phase
M1
producing either minimum
amplitude/intensity or a minimum
A1
max
3 marks; max 1 mark for two correct marking points but with n omitted
(ii) x
= λD/a = 0.030 × 5.0/0.20
C1
= 0.75 (m)
give
1 mark max for 0.75 mm but zero for 750 m
A1
(iii) 1 intensity increases by factor of 4
B1
position unchanged
B1
2 intensity unchanged
B1
distance apart of maxima is doubled
B1
3 intensity unchanged
B1
maxima move to positions of minima (and
vice versa)
B1
[11]
3. (a) (i) constant phase difference
(allow 1 mark for same phase difference or same frequency/wavelength) B2
(allow 1 mark for same phase difference or same frequency/wavelength) B2
(ii) path difference = λ/2 B1
(b) (i) evidence
shown that fringe width x = 8.0 mm B1
a = λD/x = 6.4 × 10–7 × 1.5/8.0 × 10–3 = 1.2 × 10–4 m C1
(give 2 marks for using x = 4.0 mm giving a = 2.4 × 10–4 m) A1
a = λD/x = 6.4 × 10–7 × 1.5/8.0 × 10–3 = 1.2 × 10–4 m C1
(give 2 marks for using x = 4.0 mm giving a = 2.4 × 10–4 m) A1
(ii) maximum intensity when y = 0 AND
minima at +4 and –4 B1
correct repeat distance, i.e. 8.0 mm with at least 2 full cycles drawn B1
correct repeat distance, i.e. 8.0 mm with at least 2 full cycles drawn B1
[8]
4. (i) (wave sources have) constant phase
difference (WTTE) B1
{do
not allow “in phase” but accept “same phase difference”}
(ii) difference in length between detector and
each wave source (WTTE) B1
[2]
5. (i) 1. path
diff. = nl
(where n = 0,1,2 etc) {allow 0, OR l, OR 2l etc} B1
2. path diff = (n + ½)l (where n = 0,1,etc) {allow = 0.5l OR,1.5l, etc} B1
{do not allow answers purely about
phase diff. e.g. with degrees or
p used and no ref to l}
p used and no ref to l}
(ii) recall of formula l = ax/D C1
correct
substitution for a, l
and D: e.g. ´
= (4.86 ´
10–7 ´ 2)/0.5 ´ 10–3 C1
x
= 1.94 ´
10–3 m (1.9 or 1.944) A1
(iii) central white fringe B1
other
fringes are coloured (WTTE: e.g. allow spectrum formed) B1
[7]
6. (a) (i) evidence
of good practice: i.e distance for nx measured e.g.
5x = 18mm C1
5x = 18mm C1
x = 3.6 mm (OR 3.5 OR 3.7) A1
{x = 3.4, 3.8, 3.9, 4.0, or 4 mm, implying ´ is directly
measured, and score 1 mark)
measured, and score 1 mark)
(ii) for O path difference = 0 B1
for
A path difference = 3(l) B1
for
B path difference = 1.5(l) B1
(b) recall
of l= ax/D
OR ´ =lD/a OR ´ µ l B1
l is smaller for
blue light (than red light) hence ´ is SMALLER (WTTE) B1
[7]
7. (i) constructive
interference/waves in phase for maxima
OR
destructive interference/waves ‘out of phase’ C1
maxima
produced when path difference is 0 OR nl (WTTE) A1
minima
produced when path difference is (n+1/2) l
(WTTE) A1
NB answers that do not account for
SERIES of both maxima and
minima can score maximum of 2 marks only)
minima can score maximum of 2 marks only)
(ii) recall of x = lD/a C1
{expressed in any form; allow unusual
symbols if correctly identified}
correct substitution: x = (3.0 ´ 50)/6 A1
x = 25 cm A1
(iii) microwaves vibrate/oscillate/displaced
in one plane (WTTE) B1
{do
not allow travel/propagate in one plane)
signal
decreases to zero (WTTE) B1
[8]
8. (i) wave sources with constant phase
difference B1
{NB allow “in phase” and ignore
reference to frequency/wavelength/amplitude}
(ii) S1 and
S2 ‘share the same light’ (AW) B1
reference to diffraction at the single
slit
OR to wavefronts e.g. “same wavefront reaches S1 and S2 (AW) B1
OR to wavefronts e.g. “same wavefront reaches S1 and S2 (AW) B1
(iii) Constructive
interference occurs at O B1
path difference is zero OR waves meet in phase (AW) B1
path difference is zero OR waves meet in phase (AW) B1
(iv) recall
of formula l=ax/D
in any valid form (e.g. x = lD/a) C1
{NB allow undefined symbols provided
they match the above as stated in the
spec., otherwise they must be defined}
spec., otherwise they must be defined}
correct sub. with consistent units:
l = 2 × 10–3 × 0.6 × 10–3 /1.8 C1
l = 6.7 × 10–7 m A1
l = 6.7 × 10–7 m A1
{NB allow ecf if mm used: i.e 2 marks
for 6.7 × 10–1 OR 6.7 ×
10–4}
(v) ‘fringe
separation’ (AW) would DECREASE B1
{NB allow “more fringes would be
seen”}
because x µ l (AW) B1
{NB allow ‘colour change’ arguments
for full marks:
Colour would change B1;
to a colour closer to the blue end of visible spectrum (AW) B1}
to a colour closer to the blue end of visible spectrum (AW) B1}
[10]
9. constructive interference:
valid diagram and/or explanation: e.g.
when
waves (from coherent sources) meet in phase (or nl path diff.) B1
waves
reinforce: resultant has increased displacement/amplitude B1
correctly
shown on diagram or stated
destructive
interference: valid diagram and/or explanation: e.g.
when
waves meet in antiphase/180° phase diff. {or (n + 1/2) l path diff.} B1
waves
cancel: resultant has reduced displacement/amplitude B1
correctly
shown on diagram or stated
[4]
10. diagram:
laser
OR light source and single-slit in front of double slit B1
screen
(WTTE) (or travelling microscope) behind double-slit B1
(if
‘screen’ is not labelled mark can be obtained by reference to ‘screen’ in text)
measurements:
measure
distance between double-slit and screen B1
measure
distance between neighbouring dark/bright images B1
(allow
‘fringe spacing’ or measure distance for n fringes)
formula:
recall
of l =
ax/D B1
ALL
symbols correctly defined
a
= distance between slits }
x
= fringe separation (WTTE) } B1
D
= distance between slits and screen }
(If candidate uses their own symbols
they must be used correctly to
score the formula recall mark)
score the formula recall mark)
(do
not penalise careless use of d and D: i.e. being interposed)
[6]
11. (a) DIFFRACTION B1
(b) a constant phase difference/relation (WTTE) B1
(allow
“zero phase difference” and “in phase”)
(c) constructive
interference produces bright lines AND destructive for dark lines B1
in
phase for bright AND antiphase (allow ‘out of phase’) for dark B1
(ALLOW
diagrams showing crests/troughs meeting crests/troughs for this mark)
path
difference = whole number of wavelengths {allow nl} for bright B1
(ALLOW
path difference = l
but NOT path difference = ZERO)
path
difference = odd number of half wavelengths {allow (n + 1/2) l} for dark B1
(ALLOW
path difference = ½l)
(d) recall
of l =
ax/D (in any valid form) C1
valid
substitution: e.g. ´
= (6.5 × 10 –7´ 1.5)/0.25 ´ 10–3 C1
x
= 3.9 ´
10–3 m A1
(3.9
× 10–6 scores 2 marks)
[9]
