Light as a wave Interference: light taking different paths of different lengths l adds or cancels because of different phase. constructive Dl = ml (m = 0,1,2,3…) destructive Dl = (modd )l/2

Interferometer Vary one mirror’s distance, and watch the fringes at one location change from bright to dark

In the interferometer, when the path lengths are identical we get bright light output . If light of 600 nm is used, how far back do you have to move the top mirror to make the output go dark, bright, then dark? (Be careful: if you move mirror by d, the path length changes by 2d) 300 nm 450 nm 600 nm 900 nm

Thin film interference Light reflecting from air gap between two glass microscope slides taped together.

Thin film interference Light reflecting from air gap between two microscope slides taped together.

The fringes are from an air gap between microscope slides The fringes are from an air gap between microscope slides. If the blue light is 500 nm, how much does the air gap change in thickness between the orange dots? 1500 nm 3000 nm 3500 nm 7000 nm 9000 nm Path in air has increased by ____ Thickness of air gap (d) has increased by ____

Thin film interference Reflection from the top and bottom a single film (soap bubble) Two features: l in the film is smaller than in air: The light may phase shift just by reflecting! n

Wavelength change l in the film is smaller than in air or vacuum: l = lvac/n . So we can use an effective thickness of nDx if we want to keep using lvac. l typically refers to wavelength in vacuum. If we say “light of 620 nm enters a film”, we’re referring to its wavelength in vacuum n

Reflection phase shifts “Low to high, p” “Hi to low, no” 180o (p or l/2) reflection shift when going into a higher index (slower) material.

Compare reflections on a rope

A thin film floats between two liquids A thin film floats between two liquids. In this problem how many “l/2” (p or 180o) -phase shifts are there? A. from top interface B. from bottom D. from both C. from neither What wavelengths will reflect strongly?

http://www.youtube.com/watch?v=tu3T8f-8Fgw Start at 3:26 Soap film vs time

video of turbulence in soap film above: http://media.efluids.com/galleries/interfacial?medium=518 video of turbulence in soap film

Huygen’s principle Huygen invented this idea to describe wave effects that were too hard to do with the full math! Each wave crest acts like a source of forward spherical waves. We will use it mostly to describe diffraction.

Huygen’s principle and Snell’s law Animation Left edge of wavefront strikes first. . Smaller circles form in the slower material.

Another view of Snell’s law Peaks and valleys (phase) must match at interface. Because l is different, the angles must be different.