Essential idea: Interference patterns from multiple slits and thin films produce accurately repeatable patterns.
Nature of science:
Curiosity: Observed patterns of iridescence in animals, such as the shimmer of peacock feathers, led scientists to develop the theory of thin film interference. (1.5)
Serendipity: The first laboratory production of thin films was accidental. (1.5)
Understandings:
Young’s double-slit experiment
Modulation of two-slit interference pattern by one-slit diffraction effect
Multiple slit and diffraction grating interference patterns
Thin film interference
Applications and skills:
Qualitatively describing two-slit interference patterns, including modulation by one-slit diffraction effect
Investigating Young’s double-slit experimentally
Sketching and interpreting intensity graphs of double-slit interference patterns
Solving problems involving the diffraction grating equation
Describing conditions necessary for constructive and destructive interference from thin films, including phase change at interface and effect of refractive index
Solving problems involving interference from thin films
Guidance:
Students should be introduced to interference patterns from a variety of coherent sources such as (but not limited to) electromagnetic waves, sound and simulated demonstrations
Diffraction grating patterns are restricted to those formed at normal incidence
The treatment of thin film interference is confined to parallel-sided films at normal incidence
The constructive interference and destructive interference formulae listed below and in the data booklet apply to specific cases of phase changes at interfaces and are not generally true
Data booklet reference:
Theory of knowledge:
Most two-slit interference descriptions can be made without reference to the one-slit modulation effect. To what level can scientists ignore parts of a model for simplicity and clarity?
Utilization:
Compact discs are a commercial example of the use of diffraction gratings
Thin films are used to produce anti-reflection coatings
Aims:
Aim 4: two scientific concepts (diffraction and interference) come together in this sub-topic, allowing students to analyse and synthesize a wider range of scientific information
Aim 6: experiments could include (but are not limited to): observing the use of diffraction gratings in spectroscopes; analysis of thin soap films; sound wave and microwave interference pattern analysis
Aim 9: the ray approach to the description of thin film interference is only an approximation. Students should recognize the limitations of such a visualization
A parallel beam of monochromatic light is incident on a diffraction grating with 600 lines per mm. The light is initially normal to the grating. A second order maximum is seen at an angle of 43.0˚ to the normal of the grating. Calculate the wavelength of the light used. λ = 563.8 nm
A diffraction grating with 2000 slits per centimeter is used to measure the wavelength emitted by hydrogen gas. At what angle in the first-order spectrum would you expect to find the violet line of wavelength 434 nm?
A grating with 1500 slits/cm is illuminated with light of wavelength 500 nm. What is the highest-order number that can be observed with this grating?
What is the highest-order number that can be observed if the grating has 15000 slits/cm?