Young's slits marksheme

 

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

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  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

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3.       (a)     (i)      constant phase difference
(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

(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

[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}

(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

             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)

(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

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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)

(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]