Physics 1CLecture 24B

"There are two kinds of light--the glow that illuminates, and the glare that obscures."

--James Thurber

Quiz 3 InfoIt will be a Scantron test that covers Chapters 22 and 23.

A list of equations, constants, and conversions will be provided on the quiz.

You are to write the version of your test on the Scantron form.

You will should know your Quiz Code Number that you were assigned at the first Quiz.

You are expected to abide by UC Policy on Integrity of Scholarship.

Interference in Thin FilmsHave you ever looked a soap bubble and observed patterns of different colors?

Light wave interference can also be observed in thin films (such as an oil film on water or soap bubbles).

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects off of a different medium.

Interference in Thin FilmsA light wave will undergo a phase change of 180o upon reflection from a medium of higher index of refraction than the one in which it was traveling.So, a light wave traveling in air will undergo a 180o phase shift if it reflects off an oil surface.

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

This is similar to the reflection of a transverse wave that we observed earlier off of a rigid surface.

Interference in Thin FilmsA light wave will not undergo a phase change upon reflection from a medium of lower index of refraction than the one in which it was traveling.

So, a light wave traveling in oil will not undergo a phase shift if it reflects off an air boundary.

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

This is similar to the reflection of a transverse wave that we observed earlier off of a free surface.

Interference in Thin FilmsWith light incident on a thin film we have to examine to light rays that follow the same path:Ray 1 (in air) reflects off the film surface and undergoes a phase change of 180o compared to the incident ray.

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

Ray 2 (in air) refracts at the film surface and then reflects off of Surface B (film to air) with no phase change compared to the incident wave.

Interference in Thin FilmsIn addition, ray 2 travels a distance t down and and a distance t up (for a total distance 2t). Since the extra distance that ray 2 travels is in the film medium, its wavelength will be different then in air.

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

The wavelength of light, λn, in a medium with index of refraction n is:

€

λn =λn

where λ is wavelength of light in a vacuum (air?).

Interference in Thin FilmsIn order for constructive interference to occur, the two rays must be in phase.This means that the difference in path and phase must combine to m(λ/n). Where m is 0, ±1, ±2...The difference in path is: 2tand the difference in phase is:

Constructive Interference for 1 phase change.

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

Combining all of these gives us:

€

12λn( )

€

2t − 12λn

= m λn

€

2nt = m + 12( )λ

Interference in Thin FilmsWith light incident on a thin film with another thin film of higher index of refraction below the first:

Ray 1 (in air) reflects off the film surface and undergoes a phase change of 180o compared to the incident ray.

The interference in thin films is caused by not only a path length difference but also by a phase shift as the light ray reflects

Ray 2 (in 1st film) reflects off the film surface and undergoes a phase change of 180o compared to the incident ray.

Thin Film InterferenceTo solve thin film interference problems you have to know how many phase reversals there are.Then you know which equation to use:

Equation 1 phase reversal

0 or 2 phase reversals

2nt = (m+1/2)λ constructive destructive

2nt = mλ destructive constructive

Thin Film InterferenceThin Film Interference Problem Solving strategy:1) Identify the thin film causing the interference.2) Determine the indices of refraction in the film and the media on either side of it.3) Determine the number of phase reversals: zero, one or two.4) If the interference is constructive with 0 or 2 phase reversal then use a path length difference of integral multiples of λ (use odd half multiple of λ for 1 phase reversal).

Thin Film Interference5) If the interference is destructive with 0 or 2 phase reversal then use a path length difference of odd half multiples of λ (use integral multiple of λ for 1 phase reversal).Thin film interference is used by Morpho butterflies to intensify the colors reflected.

Single Slit ExperimentA single slit placed between a distant light source and a screen produces a diffraction pattern (similar to a double slit experiment).It will have a broad, intense central band.The central band will be flanked by a series of narrower, less intense secondary bands (secondary maxima).

Single Slit ExperimentThe central band will also be flanked by a series of dark bands (minima).In general, destructive interference occurs for a single slit of width, a, when:

where m is ±1, ±2, ±3...

You can observe the first minima at the angle:

€

sinθ =mλa

€

θ = sin−1 λa⎛

⎝ ⎜ ⎞

⎠ ⎟

Single Slit ExperimentThe cause of single slit interference is path length difference (just like double slit interference).In the single slit case, each portion of the slit acts as a source of waves.The light from one portion of the slit can interfere with light from another portion of the slit.

You can again use the approximation:

€

sinθ =yL

Single Slit InterferenceExampleLight of wavelength 750nm passes through a slit 1.00μm wide. How wide is the central maximum in centimeters, on a screen 20.0cm away?

AnswerFirst, you must define a coordinate system.The center of the central maximum is considered y=0.

w

Single Slit InterferenceAnswerWe can easily calculate the angle θ from the centerline to the first minima, m=1, by:

€

sinθ =mλa

€

sinθ =1( )7.5 ×10−7m1.0 ×10−6m

= 0.75

€

θ = sin−1 0.75( ) = 48.6°

We can find the length from the centerline to the first minima by taking:

€

tanθ =yL

€

y = L tanθ = 20 cm( ) tan 48.6°( ) = 22.7 cm

But since this is only half the central maximum width, we must double it; such that: w = 2y = 45.4cm.

Clicker Question 24B-1Upon reflection, light undergoes a 180o phase change:

A) always.

B) never.

C) if the incident medium has the lower index of refraction.

D) if the incident medium has the higher index of refraction.

E) whenever the incident angle is less than the critical angle.

For Next Time (FNT)

Start reading Chapter 25

Finish working on the homework for Chapter 23