Today 1/27  HW: 1/27 Handout “Anti-Reflection Coating” due Thursday 1/30  Today: Reflections at Boundaries 27.3  Thin Film Interference 27.3  Labs start Today  Peer Guidance Center still need Monday afternoon covered

Next Week’s Lab: Microwaves  A wave in the “electric field”  Reflection and transmission from and through wood  Reflection from metal (why metal is bad in your microwave)  Polarization (see section 24.6)  Interference (Young’s Double Slit)

Light to Heavy Both transmission and reflection Boundary feels like a fixed end to the light string Reflection just like fixed end, inverted Transmitted wavelength has the same shape except it’s shorter in length because it travels slower than the incoming wave. Slower, so not as far from boundary Shorter, “bunched up”Inverted wave

Heavy to Light Both transmission and reflection Boundary feels like a free end to the heavy string Reflection just like free end, not inverted Faster, farther from boundary Longer, “spread out”Wave not inverted Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave.

Slower, so not as far from boundary Shorter, “bunched up”Inverted wave Faster, farther from boundary Longer, “spread out”Same as incoming wave Light: GlasstoAir Light: AirtoGlass

Thin Films Eyeball Two reflections, front and back = two sources!

Thin Films A radio antenna broadcasts at a frequency of 93.7  MHz ( = 3.2 m). A “mirror” 1.6  m away reflects the signal. Where is the reception good along the dotted line? PLD = ? at the X PLD = all along the dotted line so constructive everywhere. (= ) 1.6 m

Thin Films 1.6 m Crest lines up with crest and the waves arrive in phase, constructive interference. Now move the mirror back A radio antenna broadcasts at a frequency of 93.7  MHz ( = 3.2 m). A “mirror” 1.6  m away reflects the signal. Where is the reception good along the dotted line? Trough in Trough out

Thin Films Twin radio antennas broadcast in phase at a frequency of 93.7  MHz ( = 3.2 m). Crest lines up with trough and the waves arrive out of phase, destructive interference. Now cause a “phase shift” at the boundary, turn crest into trough 2.4 m Now move the mirror back Trough in Trough out

Thin Films Twin radio antennas broadcast in phase at a frequency of 93.7  MHz ( = 3.2 m). Crest lines up with crest and the waves arrive in phase, constructive interference. Now cause a “phase shift” at the boundary, turn crest into trough 2.4 m Phase shifted Trough in Crest out

Thin Films Eyeball Wavelength ( ) Film thickness (PLD) Different in film Phase shifts at boundaries Interference

Index of refraction (n) Light slows down as it passes through glass, water, or any clear material. Index of refraction says how much. When the wave slows down it gets “bunched up” and has a shorter wavelength. When the wave exits the medium it returns to its original speed and wavelength.

Finding in materials n 2 = 1.33 Wavelength is shorter but frequency is the same in any material. n 1 = 1.0 v 1 = c/n 1 = c = 3 x 10 8 m/s v 2 = c/n 2 = 2.3 x 10 8 m/sWaves obey the equation: v = f If v changes by a factor 1/n and f remains constant then must change by the factor 1/n also. 2 = 1 /n 2 Just a proportion

Example Light with = 675 nm enters glass with n = 1.5. What is the wavelength in the glass? glass = /n glass = 675 nm/1.5 = 450 nm What is the wavelength after it exits the glass? = 675 nm

Thin Films Eyeball The wavelength is different in the film. Wavelength ( ) Film thickness (PLD) Index of refraction (n) Phase shifts at boundaries

Thin Films Eyeball PLD = 2t, t = film thickness Wavelength ( ) Film thickness (PLD) Index of refraction (n) Phase shifts at boundaries t

Thin Films Phase shifts - the tricky part Sometimes reflections include phase shifts upon reflection Crest in crest out = no phase shift Crest in trough out = 1/2 phase shift AirGlass Phase Shift? Yes, bouncing off higher n Phase Shift? No, bouncing off lower n Air