Phys. 122: Tuesday, 08 Sept.Phys. 122: Tuesday, 08 Sept.

Mast. Phys.: Assign. 1 due this evening. Assign. 2 isavailable and is due in one week. Written HW 3: due Thursday. Written HW reminder: Assigned problems are the“Exercises and Problems,” NOT the “ConceptualQuestions,” which often (confusingly) have the same

numbers. Reading: Should have finished ch. 22. Begin ch. 25next and finish reading by next Tuesday (15 Sept.).

HW hints needed?

We can use superpositionin a fancy way in order toexplain why a fixed endreflects a wave pulseupside-down.

Standing Waves

(On a string with twofixed ends, or an organpipe with two fixed ends,etc.):

f_n = n f_1

...with f_1 = v/(2L)

and n = 1,2,3,...

Two-source interference

Clickers: Sound of a single frequency iscoming from two speakers, producing

interference. If the frequency goes up, whathappens to the destructive (quiet) zones in

the room?• a) They get closer together.

• b) They move farther apart.

• c) They remain in the same place.

• d) They move, and get louder. e) They move upward also (against gravity).

Beats: f_b = | f_1 – f_2 |

Unlike interference at certain points in space fromtwo sources emitting the same frequency, beats areinterferences at certain points in time from slightlydifferent frequencies.

Musicians often tunetheir instruments bytrying to make thebeats disappear whenplayed at the sametime as a referencealready-tunedinstrument.

Why is the top of this reflection dark? Thesoap film is thin there, and there's a phase flipfrom the reflection on one side.

Phase flips when reflecting from a LARGERindex of refraction. Similar to waves movingto a thicker (slower wave speed) string:

Thin-film interferenceis responsible for thecolors seen reflectedfrom an oil slick,soap bubble, and manyother things in nature(e.g., peacock feathers!).Constructive interferencebetween the reflections fromthe two surfaces give a brightcolor in the reflection.

Thin transparent films, placed on glass surfaces, such as lenses, can control reflections from the glass.

Antireflection coatings on the lenses in cameras, microscopes, and other optical equipment are examples of thin-film coatings.

Application: Thin-Film Optical Coatings

Slide 21-96

Thin-film interference:

Path difference = 2 d (d = film thickness)... should be either = (m) λ/n or = (m+ ½) λ/n

which depends upon whether we'relooking at reflection or transmission, andwhether destructive or constructive, and howmany phase flips there are, so it's best to workit out for each individual case. (Here, λ is thewavelength in vacuum.)

Clickers: Suppose that the soap film has airon one side, and glass on the other. How

will the (reflected) thinnest part of the film appear? a) It will be dark. b) It will be bright. c) Whether it is bright or dark will depend upon the color of the light.

•d) Whether it is dark or bright will depend upon the direction the light comes from.

•e) Whether it is dark or bright will depend upon the thickness of the glass and the air.

Clickers: Okay, why was our soap filmbright in the thinnest portion?

a) Physics demos never go as planned b) There were no phase flips c) There was only one phase flip d) There were two phase flips e) There was glass on one side

Clickers: Interference can only be seen for coherentwaves. What are coherent waves? a) Waves from earthquakes b) Waves from tropical storms c) Waves from stereo sound systems d) Waves whose speeds are all related e) Waves whose phases are all related

Two-source interference

Clickers: Visible light has wavelengths thatare a few....

a) kilometers

b) millimeters

c) tenths of micrometers

d) Ångstroms (tenths of nanometers)

e) attometers

For large L, the distances to the two sources aredifferent by d sin θ. It will be useful later tonotice that tan θ = y/L.

Two-source interference

Negative m values are also allowed!

For small angles, we can use the approximationsin θ ≈ tan θ. If measured in radians, both of theseare also approximately θ itself (for small angles)!In that case, we can replace sin θ by y/L.