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Question 19N.2.HL.TZ0.10

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Date November 2019 Marks available [Maximum mark: 11] Reference code 19N.2.HL.TZ0.10
Level HL Paper 2 Time zone TZ0
Command term Calculate, Discuss, Draw, Estimate, Predict, State Question number 10 Adapted from N/A
10.
[Maximum mark: 11]
19N.2.HL.TZ0.10

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

(a)

Predict whether reflected ray X undergoes a phase change.

[2]

Markscheme

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

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

(b(i))

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

[1]

Markscheme

2d ✔
NOTE: Accept 2dn

(b(ii))

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

[2]

Markscheme

2dn=λ2 ✔

d=«λ4n=6564×1.38=» 119 «nm» ✔

 

NOTE: Award [2] for bald correct answer

(b(iii))

discuss a practical advantage of this arrangement.

[2]

Markscheme

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

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.

(c(i))

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

[2]

Markscheme

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(ii))

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]

Markscheme

use of θ=1.22λb✔

θ=2.9×10-4 «rad» ✔

 

NOTE: Award [2] for bald correct answer

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