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BPhO R1 S1 · Section 1

Interference

5 questions — reveal each final answer.

2012 · pInterference

A soap bubble, diameter $3.0 \mathrm{~cm}$, containing helium floats in the air. Determine the thickness of the bubble, as a multiple of the wavelength, $650 \mathrm{~nm}$, of red light, assuming soap solution has a density of $1.00 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$. The density of the air and helium are, respectively, $1.28 \mathrm{~kg} \mathrm{~m}^{-3}$ and $0.18 \mathrm{~kg} \mathrm{~m}^{-3}$. [4]

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Final result
  • The film is about $8.5$ wavelengths of red light thick ($t \approx 5.5\,\mu\text{m}$).

Worked solutions are in the book.

2017 · nInterference

A thin film of transparent material of refractive index $1.52$ and thickness $0.42 \mu \mathrm{m}$ forms a thin coating on glass of refractive index 1.60. It is viewed by reflection with white light at normal incidence. What visible wavelength in vacuo is most strongly reflected? [5]

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Final result
  • Because both reflections share a $\pi$ shift, the condition is $2nt = m\lambda$.

Worked solutions are in the book.

2017 · oInterference

Monochromatic light of wavelength $600 \mathrm{~nm}$ is incident on two vertical slits hence producing two coherent sources. Before the light leaving these slits overlaps and interferes, each beam passes through a tube $5.0 \mathrm{~cm}$ long. One of the tubes is now gradually evacuated and it is noted that the fringe pattern shifts 25 fringes. Calculate the refractive index of air. [5]

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Final result
  • The refractive index of air is $1.0003$, the standard value.

Worked solutions are in the book.

2018 · oInterference

A narrow beam of monochromatic light falls on a diffraction grating of 1200 lines $\mathrm{mm}^{-1}$, and two diffracted beams of successive orders are observed at $14^{\circ}$ and $73^{\circ}$ to the normal, both of them on the same side of the normal. The incident beam of light is not along the normal to the grating.

(i) Sketch a diagram to show the path difference between rays passing through adjacent slits, for a ray incident on the diffraction grating at angle $\theta_{1}$, and for the corresponding ray emerging from the grating at angle $\theta_{2}$, with respect to the normal.

(ii) Derive an equation relating the angles $\theta_{1}$ and $\theta_{2}$ to the order of diffraction, $n$, and the wavelength, $\lambda$.

Determine:

(iii) The wavelength of the light used.

(iv) The angle of incidence of the beam on the grating.

(v) The angle of diffraction of a third transmitted beam. [6]

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Final result
  • The wavelength is $595\ \text{nm}$ and the incidence angle is $28^\circ$; the $14^\circ$ and $73^\circ$ beams are the $n=1$ and $n=2$ orders.

Worked solutions are in the book.

2020 · lInterference

A narrow beam of monochromatic light is passed normally through a diffraction grating of $6 \times 10^{5}$ lines per metre. Three spots of light are observed on a screen placed $80 \mathrm{~cm}$ away from the grating, and the outer spots are $30 \mathrm{~cm}$ away from the central spot. Determine the wavelength of the light used. [2]

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Final result
  • The wavelength is $585 \, \text{nm}$, in the visible (orange) range, consistent with three observed spots: the central maximum plus a single first order on each side.

Worked solutions are in the book.

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