1. ConcepTest #37: An electromagnetic wave travels from region 1 with index of refraction n 1 into region 2 with index of refraction n 2. The index of refraction in region 1 is smaller than the index of refraction in region 2 (n 1 < n 2 ). Consider the following choices: a)Where is the speed of the electromagnetic wave faster? Next week, we’ll see that the frequency of the electromagnetic wave is the same in both regions. b)Where is the wavelength of the electromagnetic wave larger?

2. ConcepTest #38: Consider light that is incident (i) on the interface between one medium and another, with n 1 < n 2. We saw previously that when a wave goes from one medium into another, part of the wave could be reflected (r) and part of the wave could be transmitted (t). Which of the following is true about the reflected wave in this case? 1. No reflected wave 2. Reflected wave inverted with respect to incident wave 3. Reflected wave NOT inverted with respect to incident wave 4. Not enough info

3. ConcepTest #39: Light in air is normally incident onto a thin film of oil (thickness 500 nm) spread on glass, as shown. (In the figure, the rays are drawn at angles other than straight down and straight up for some clarity.) The indices of refraction are n oil = 1.20 and n glass = 1.50. Which of the following is the geometrical path length difference between the light wave reflected from the air-oil interface and the light wave reflected from the oil- glass interface?

4. Example: Colors in Thin Film Interference Light in air is normally incident onto a thin film of oil (thickness 500 nm) spread on glass, as shown. The indices of refraction are n oil = 1.20 and n glass = 1.50. Which wavelengths of light are most strongly reflected?

5. TWO (Source, Slit, Wave, Phasor) Interference Two waves  two phasors Same amplitude Same frequency/wavelength Totally Constructive Interference “brightest”; “loudest”; “highest”; “most intense”; “strongly reflected”; etc. Totally Destructive Interference “dimmest”; “softest”; “lowest”; “least intense”, etc.

6. ConcepTest #40: A (triangular) thin film of oil is surrounded by air on all sides. Visible light is reflected from (essentially) normal incidence from the “top” of the film and from the “bottom” of the film. Consider the following choices: a)What color will you see at the left (thinnest) edge of the film? b)Starting from the left end of the film and moving to the right, what is the next color you will see?

7. Example: More Colors in Thin Films A (triangular) thin film of oil is surrounded by air on all sides. Visible light is reflected from (essentially) normal incidence from the “top” of the film and from the “bottom” of the film. To see reflection, must have The thin film has a maximum thickness of 1700 nm and index of refraction 1.40. How many red bands will you see (in normal incidence)?

8. ConcepTest #41: Two speakers are driven by the same amplifier, and are 3 m apart as shown. Point A is 4 m away from the line connecting the speakers, along the bisector of that line. Point B is 4 m directly in front of one of the speakers. Consider the following choices for the amplitude of the combined waves from both speakers (use v sound = 340 m/s) : 1. Maximum2. Minimum 3. Neither max 4. Not enough info nor. min 3 m A ● B ● a)frequency = 340 Hz, amplitude at A? b)frequency = 340 Hz, amplitude at B? c)frequency = 170 Hz, amplitude at A? d)frequency = 170 Hz, amplitude at B?

9. x2x2 d Two Slit/Two Source Interference in the “far-field” regime: Young’s Double Slit Experiment & Fraunhofer Limit. Uniform slits, distance d apart. Light of wavelength. Screen L away L  y “Thin” slits  (width of slit small compared to distance between slits; more on slit width Friday) x1x1

10. “Far field” limit, continued. Special case: L >> d  x 1 essentially parallel to x 2. x2x2 x1x1 d  Path length difference between adjacent slits

11. For MAXIMUM amplitude of combined waves (“totally constructive interference”) from two sources, need: Locations of maxima  Evenly spaced. Two-Slit/Source Interference Maximums and Minimums (Far Field) For MINUMUM amplitude of combined waves (“totally destructive interference”) from two sources, need: Locations of minima  Evenly spaced between maxima.

12. Maximum? Now have THREE phasors Three Slit/Source Interference? Identical to before; including positions of “primary” maxima Minima? Try results in: NOT completely destructive! Can three phasors  zero?