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Thin Films & Interference

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1 Thin Films & Interference
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2 Thin Films Everyone, at some point, has witnessed thin film interference It occurs when you see the colour spectrum in gasoline or oil that has been spilled or in a soap bubble The effect occurs due to optical interference

3 How does it work? Consider a horizontal film like a soap bubble that is extremely thin, compared to the wavelength of light direction at it from above. Some is reflected Some is refracted

4 How does it work? The light rats that were refracted, and then reflected have travelled a longer distance ∆L causes light waves to go out of phase This results in destructive interference that is hitting our eye

5 Real-world examples: Soap bubbles Oil ….also “Newtons Rings”
Bowl of water on top of reflective glass When you look into the bowl you see a series of rings from constructive and destructive interference

6 Recall from Gr. 11 Properties of reflected waves
Fixed end (less dense medium to a move dense medium) Free end (more dense medium to a less dense medium) Ring so that the spring can move up and down…

7 3-Cases for Thin Film Interference-Reflected Light
Remember: transmitted light wave are always in phase from the source Comparing film thickness (t) to the wavelength of light ( ) For t << For t = / for t = /2 *fill so thin that *to go across the film *to go across film it has *Minimal time lag and back is ½ lamda travelled an extra whole Wave reflects back like *wave travels ½ *back to desctructive a fixed end (crest=trough) so the wave shifts interference Destructive interference *constructive interference Hit this dashed line at the same time

8 Summary for Reflected Light
Constructive interference occurs when: λ / λ /2 (n – 1) Started at λ/4 and occurs every 1/2λ n is the maximum (if n = 1, then…..) = λ/4 + 2λ(n-1)/ *common denominators = ¼ (λ + 2λn – 2λ) = λ(2n – 1)/4 Destructive interference occurs when: 0λ + λ/2 (n – 1) 0λ , λ/2, λ, ……started at 0 and occurs every 1/2λ = λ(n – 1) /2

9 3-Cases for Thin Film Interference – Transmitted Light
Now interested in light on the other side Remember: transmitted waves are always in phase from the source Comparing film thickness to the wavelength of light For t << For t = λ/ For t = λ/2 *constructive *blue line is no longer a *shift by a wavelength Interference crest b/c it has been shifted ½ wavelength Crest Reflects as atrough Reflects as a crest Reflects as a trough Transmits as a crest

10 Summary for Transmitted Light
Opposite to the reflected light formulas Constructive interference occurs when: = λ(n-1)/2 Destructive interference occurs when: λ(2n – 1) /4

11 Equations for Thin Film Interference
From v = fλ, we know v is the speed of light So, c = fλ. If we assume the initial equation is the velocity of light in a different medium then we can take a ratio of c/v: c = f1λ f1 = f2 because it is coming from v f2λ the same source c = λ ….and we know n = c/v v λ2 n = λ1 λ2

12 Practice In the summer, the amount of solar energy entering a house needs to be minimized. We do this by applying a thin film coating to maximize reflection of light. If light (assume λ = 578 nm) travels into an energy-efficient window, what thickness of the added coating (n = 1.4) is needed to maximize reflected light? “minimized” tells us that it is destructive interference need to find the wavelength in the new film t= n = λ1/λ t = λ(2n – 1)/4 (n =1 *max) λ1 = n = **realistically that is too thin to apply, can “ramp it up” by increasing n to 10, etc. to get a thickness you can actually apply


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