A thin uniform film of refractive index 1.750 is placed on a...

A thin uniform film of refractive index 1.750 is placed on a sheet of glass of refractive index $1.50 .$ At room temperature $\left(20.0^{\circ} \mathrm{C}\right)$, this film is just thick enough for light with wavelength $582.4 \mathrm{nm}$ reflected off the top of the film to be cancelled by light reflected from the top of the glass. After the glass is placed in an oven and slowly heated to $170^{\circ} \mathrm{C},$ you find that the film cancels reflected light with wavelength $588.5 \mathrm{nm} .$ What is the coefficient of linear expansion of the film? (Ignore any changes in the refractive index of the film due to the temperature change.

Key Concepts

Thermal Expansion

Thermal expansion explains how the physical dimensions of materials change with temperature. In the context of thin films, an increase in temperature causes the film to expand, altering its thickness. This change in thickness, in turn, modifies the optical path length and shifts the interference conditions, which can be used to calculate the coefficient of linear expansion of the film.

Phase Change upon Reflection

When light reflects from a boundary between materials of differing refractive indices, it may undergo a phase change. For example, if light reflects from a medium with a higher refractive index than the incident medium, a half-wavelength phase shift occurs. The understanding of these phase shifts is crucial in determining the interference pattern in thin films.

Thin Film Interference

This concept deals with the interference of light waves reflected from the different boundaries of a very thin film. The constructive or destructive interference observed is determined by the optical path difference between the waves, including any phase shifts that occur upon reflection. In many cases, one reflection may incur a half-wavelength (?) phase shift which is necessary to correctly set up the interference conditions.

Optical Path Length

The optical path length, defined as the product of the physical thickness of the film and its refractive index, is key to determining the phase difference between reflected light waves. It essentially represents the effective distance light travels in the medium and is central to calculating the interference condition (for example, matching multiples of half-wavelengths for destructive interference).

Transcript

00:01 Peso.

00:01 Here we have a team unit from film off.

00:06 Factoring example uncertain fight on blue.

00:09 This is a glass of effective next amplified.

00:11 So light incident on the film.

00:13 Eric looks from the top surface off the film on under one from the top surface off the glass.

00:19 Right now, these two weeks cancel out each other on dhe.

00:25 There's the construct people.

00:26 Indifference, constructive or destructive interference is formed at the cancel out the nancy check it.

00:32 So now this wave here, uh, this way here reflects from a denser 1,000,000.

00:39 Right? so there is a change in face, whereas this way reflects from model medium.

00:43 Because this has one punch and part.

00:45 This has not been fight.

00:46 So if extra morey allen williams.

00:48 So there is not an infant.

00:49 So one of the whips have changed has changed this changing face.

00:54 So the condition far so the condition for a destructive interpret inside we need to secure interference.

01:03 Oh, yeah.

01:03 We need to cancel out the refrigerator for the destructive interference.

01:07 The condition is two times t is equality m times.

01:13 Right now in this case here, when deputies tragically so tee times too trendy is equal to m times.

01:24 So lamda is actually the lambda off.

01:28 Women's off right inside the food lambda.

01:31 Right? so and lambda is giving us sometimes number was not linda.

01:38 Upon the refractive index off the i said this is a christian one on dde after the glass is based in over...

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