Phys. 122: Tuesday, 08 Sept. Mast. Phys.: Assign. 1 due this evening. Assign. 2 is available and is due in one week. Written HW 3: due Thursday. Written HW reminder: Assigned problems are the “Exercises and Problems,” NOT the “Conceptual Questions,” which often (confusingly) have the same numbers. Reading: Should have finished ch. 22. Begin ch. 25 next and finish reading by next Tuesday (15 Sept.).

HW hints needed?

We can use superposition in a fancy way in order to explain why a fixed end reflects a wave pulse upside-down.

Standing Waves (On a string with two fixed ends, or an organ pipe 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 is coming from two speakers, producing interference. If the frequency goes up, what happens 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 from two sources emitting the same frequency, beats are interferences at certain points in time from slightly different frequencies. Musicians often tune their instruments by trying to make the beats disappear when played at the same time as a reference already-tuned instrument.

Why is the top of this reflection dark? The soap film is thin there, and there's a phase flip from the reflection on one side.

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

Thin-film interference is responsible for the colors seen reflected from an oil slick, soap bubble, and many other things in nature (e.g., peacock feathers!). Constructive interference between the reflections from the two surfaces give a bright color 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're looking at reflection or transmission, and whether destructive or constructive, and how many phase flips there are, so it's best to work it out for each individual case. (Here, λ is the wavelength in vacuum.)

Clickers: Suppose that the soap film has air on 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 film bright 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 coherent waves. 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 that are 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 are different by d sin θ. It will be useful later to notice that tan θ = y/L.

Two-source interference Negative m values are also allowed! For small angles, we can use the approximation sin θ ≈ tan θ. If measured in radians, both of these are also approximately θ itself (for small angles)! In that case, we can replace sin θ by y/L.