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**The Wave Nature of Light Thin Film Interference**

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**Objectives, you should be able to:**

Understand the principles of refraction Apply the principles of interference to light reflected by thin films

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**Thin Film Interference**

Interference also occurs as waves travel through different media. If there is a very thin film of material – a few wavelengths thick or less – light will reflect from both the bottom and the top of the layer, causing interference. Examples: soap bubbles and oil slicks

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**Refraction (Bending) of Waves**

Waves propagate more slowly in the medium of higher index of refraction. This leads to a bend in the wavefront. The frequency of the light does not change, but the wavelength does as it travels into a new medium.

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Index of Refraction The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium: so always!

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**Thin Film Interference**

Get two waves by reflection off of two different interfaces. 1 2 n0=1.0 (air) n1 (thin film) Ray 2 travels approximately 2t further than ray 1. t n2 *Film thickness must be on the order a few or less Constructive interference: wave that travels through the film & back must have traveled just the right distance such that it is in phase

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**Thin Film Interference**

In addition to thickness of film (distance) light reflects off a surface of higher index of refraction, a 180° phase shift occurs (n1<n2) Light in air reflecting off just about anything (glass, water, oil, etc.) will undergo a 180° shift. When n1>n2, no phase shift occurs light in oil, which has a higher n than water does, will have no phase shift Note a shift by 180° is equivalent to the wave traveling a distance of half a wavelength.

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**Constructive Interference:**

Phase shift at surface ½, reflection from oil/water no phase shift and travels ½ [If film thickness was ½ , then travel 1 and would be destructive (off by ½ )]

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**Non-reflective coatings Destructive Interference:**

Phase shift at air surface, reflection from coating/lens phase shift ½ and travels ½ (off by ½ ) (If film thickness was ½ , then travel 1 and would be constructive)

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**Constructive or Destructive**

Determine d, number of extra wavelengths for each ray. 1 2 n = 1.0 (air) n1 (thin film) t n2 Note: this is wavelength in film! (lfilm= lo/n1) This is important! Reflection Distance Ray 1: d1 = 0 or ½ Ray 2: d2 = 0 or ½ + 2 t/ lfilm If |(d2 – d1)| = 0, 1, 2, 3 … (m) constructive If |(d2 – d1)| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

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**Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 d1 = ½**

Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? d1 = ½ Reflection at air-film interface d2 = 0 + 2t / lglass = 2t nglass/ l0= 1 Phase shift = d2 – d1 = ½ wavelength

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**Equations for Thin Film Interference (if you an equation kind-of person)**

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**A thin film of gasoline (ngas=1. 20) and a thin film of oil (noil=1**

A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength… t = l nwater=1.3 ngas=1.20 nair=1.0 noil=1.45 The gas looks: bright dark d1,gas = ½ d2,gas = ½ + 2 The oil looks: bright dark | d2,gas – d1,gas | = 2 constructive d1,oil = ½ d2,oil = 2 | d2,oil – d1,oil | = 3/2 destructive

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**Different colored lines**

different locations of the film may be of appropriate thickness to reinforce different colors of light (different )

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**Interference by Thin Films**

One can also create a thin film of air by creating a wedge-shaped gap between two pieces of glass. m =1 m =2 m =3 B R I G H T B R I G H T D A R K D A R K D A R K

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Newton’s Rings interference is seen when a planoconvex lens is placed on top of a flat glass surface The air film between the glass surfaces varies in thickness from zero at the point of contact to some thickness t A pattern of light and dark rings is observed This rings are called Newton’s Rings The particle model of light could not explain the origin of the rings

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**2nt = (m + ½ ) λ t = (m + ½ ) λ / 2n t= ½ (550) / 2 (1.38) = 99.6 nm**

An antireflective coating (n=1.38) is coated on a plastic lens (n=1.55). It is desired to have destructive interference for =550nm (center of visible spectrum). What is the thinnest film that will do that? How many phase changes? (air-film-glass) 2 (both surfaces low to high n) Equation for destructive for 2 phase changes Solve for t (m=0 for thinnest) 2nt = (m + ½ ) λ t = (m + ½ ) λ / 2n t= ½ (550) / 2 (1.38) = 99.6 nm

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**Interference by Thin Films**

Problem Solving: Interference Interference occurs when two or more waves arrive simultaneously at the same point in space. Constructive interference occurs when the waves are in phase. Destructive interference occurs when the waves are out of phase. An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.

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Announcements HW set 9 due this week; covers Ch 23 and Ch 24.1-4 Office hours: My office hours Th 2 -3 pm or make an appointment Come to class April 19.

Announcements HW set 9 due this week; covers Ch 23 and Ch 24.1-4 Office hours: My office hours Th 2 -3 pm or make an appointment Come to class April 19.

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