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Date November 2019 Marks available 1 Reference code 19N.2.HL.TZ0.10
Level Higher level Paper Paper 2 Time zone 0 - no time zone
Command term State Question number 10 Adapted from N/A

Question

The lens of an optical system is coated with a thin film of magnesium fluoride of thickness d. Monochromatic light of wavelength 656 nm in air is incident on the lens. The angle of incidence is θ. Two reflected rays, X and Y, are shown.

The following refractive indices are available.

Air                            = 1.00
Magnesium fluoride = 1.38
Lens                         = 1.58

The thickness of the magnesium fluoride film is d. For the case of normal incidence (θ = 0),

Light from a point source is incident on the pupil of the eye of an observer. The diameter of the pupil is 2.8 mm.

Predict whether reflected ray X undergoes a phase change.

[2]
a.

state, in terms of d, the path difference between the reflected rays X and Y.

[1]
b(i).

calculate the smallest value of d that will result in destructive interference between ray X and ray Y.

[2]
b(ii).

discuss a practical advantage of this arrangement.

[2]
b(iii).

Draw, on the axes, the variation with diffraction angle of the intensity of light incident on the retina of the observer.

[2]
c(i).

Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.

[2]
c(ii).

Markscheme

there is a phase change ✔
of π OR as it is reflected off a medium of higher refractive index ✔

a.

2d
NOTE: Accept 2dn

b(i).

2dn=λ2 

d=«λ4n=6564×1.38=»119«nm» ✔

 

NOTE: Award [2] for bald correct answer

b(ii).

reflection from «front surface of» lens eliminated/reduced
OR
energy reaching sensor increased ✔

at one wavelength ✔

NOTE: Accept reference to reduction of glare for MP1

b(iii).

standard single slit diffraction pattern with correct overall shape ✔

secondary maxima of right size ✔

 

NOTE: Secondary maximum not to exceed 1/5th of maximum intensity

Ignore width of maxima

c(i).

use of θ=1.22λb

θ=2.9×10-4 «rad» ✔

 

NOTE: Award [2] for bald correct answer

c(ii).

Examiners report

[N/A]
a.
[N/A]
b(i).
[N/A]
b(ii).
[N/A]
b(iii).
[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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