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Date May 2021 Marks available 1 Reference code 21M.2.HL.TZ2.8
Level Higher level Paper Paper 2 Time zone 2
Command term Show that Question number 8 Adapted from N/A

Question

Monochromatic light of wavelength λ is normally incident on a diffraction grating. The diagram shows adjacent slits of the diffraction grating labelled V, W and X. Light waves are diffracted through an angle θ to form a second-order diffraction maximum. Points Z and Y are labelled.

  

State the effect on the graph of the variation of sin θ with n of:

State the phase difference between the waves at V and Y.

[1]
a.i.

State, in terms of λ, the path length between points X and Z.

[1]
a.ii.

The separation of adjacent slits is d. Show that for the second-order diffraction maximum 2λ=dsinθ.

[1]
a.iii.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

[4]
b.

using a light source with a smaller wavelength.

[1]
c.i.

increasing the distance between the diffraction grating and the screen.

[1]
c.ii.

Markscheme

0 OR 2π OR 360°

 

a.i.

4λ

a.ii.

sinθ«=XZVX»=4λ2d


Do not award ECF from(a)(ii).

a.iii.

identifies gradient with λd OR use of dsinθ=nλ ✓

gradient = 0.08 OR correct replacement in equation with coordinates of a point 

d=633×10-90.080=«7.91×10-6 m» 

1.26×102 OR 1.27×102«mm-1» 


Allow ECF from MP3

b.

gradient smaller 

c.i.

no change

c.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
a.iii.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Additional higher level (AHL) » Topic 9: Wave phenomena » 9.3 – Interference
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Additional higher level (AHL) » Topic 9: Wave phenomena
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