Today: Sect Thin-film interference Sect Diffraction gratings Wednesday: Chapter 29 Relativity!

A train of waves of fixed frequency is traveling along a thin, light cord toward the juncture to a heavy, thick cord. Both cords are stretched taut and under the same tension. The waves that travel across the heavy cord will have 1) greater speed than along the lighter cord. 2) the same speed as along the lighter cord. 3) smaller speed than along the lighter cord.

A train of waves of fixed frequency is traveling along a thin, light cord toward the juncture to a heavy, thick cord. Both cords are stretched taut and under the same tension. The waves traveling across the heavy cord have 1) larger wavelength than along the lighter cord. 2) the same wavelength as along the lighter cord. 3) smaller wavelength than along the lighter cord.

air glass air Direction of electric & magnetic fields invert, undergoing a 180 o phase shift No phase shift! Preserves E, B field directions upon reflection.

air glass n=1.5 water n=1.3 Direction of electric & magnetic fields invert, undergoing a 180 o phase shift Direction of electric & magnetic fields invert, undergoing a 180 o phase shift

air n=1.00 oil n=1.38 water n=1.33 Direction of electric & magnetic fields invert, undergoing a 180 o phase shift No phase shift! Preserves E, B field directions upon reflection.

Another way to get Interference l Thin oil film on water: çPart of the incoming light is reflected off the top surface (point A), part at the lower surface (point B). çLight traveling through oil travels extra distance (from A to B to C).  If this distance is  2  3  4  … »constructive interference!  If this distance is  2  3  2  5  2  … »destructive interference!

air water n=1.33 t If 2t = exactly 1 or any whole number multiple of a wavelength 2t = m the two waves would combine oil film n=1.38 a. in phase and constructively interfere b. out of phase and destructively interfere.

air water n=1.33 t If 2t = exactly 1/2 or any whole number multiple of a wavelength 2t = (m+1/2) the two waves would combine soap film n=1.25 a. in phase and constructively interfere b. out of phase and destructively interfere.

Non-reflecting lenses The blue-purple tint of camera and binocular lenses is due to a think coating intended to make them “invisible” or at least reduce reflections… not by making them less “shiny” but by the destructive interference of the reflected light! Air, n O  1.00 Thin film, n 1 Glass lens, n o phase on each reflection destructive interference constructive interference but this of course works exactly for only 1 precise wavelength!

A glass ( n=1.60 ) lens is coated with a thin film of fluoride (MgF 2, n=1.38 ). What minimum film thickness makes =550 nm light non-reflecting? 180 o phase change for each reflection t = /4

Diffraction Gratings Surface machine scored with many parallel scratches 5000 lines /cm Spacing d = 1 cm/5000 = 2  cm

dsin  = m m = 0,  1,  2,  3, … m = 0

dsin  = m sin  = m /d

3) smaller speed than along the lighter cord. 3) smaller wavelength than along the lighter cord. b. out of phase and destructively interfere.