IB Physics-Qc#13 -Paper 2-Thin film interference and Resolution HL

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
Predict whether reflected ray X undergoes a phase change.
The thickness of the magnesium fluoride film is d. For the case of normal
incidence (θ = 0), state, in terms of d, the path difference between the reflected rays X and
Y.
c. calculate the smallest value of d that will result in destructive
interference between ray X and ray Y.
d. discuss a practical advantage of this arrangement.
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.
e. Draw, on the axes, the variation with diffraction angle of the intensity of
light incident on the retina of the observer.
f. 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.
Topic 4 and topic 9 Oscillations and waves playlist: