1 W14D2: Interference and Diffraction Experiment 6 Today’s Reading Course Notes: Sections

Announcements PS 11 is only for practice. It will not be graded. Next Reading Assignment W14D3 Course Notes: Sections Final Exam Mon May 20 9 am-12 noon in Johnson Athletic Center Review Sessions TBA 2

3 Outline Review Interference Diffraction Interference and Diffraction Experiment 6

4 Interference – Phase Shift What can introduce a phase shift? 1.From different, out of phase sources 2.Sources in phase, but travel different distances because they come from different locations constructivedestructive

5 Microwave Interference

6 Review The Light Equivalent: Two Slits

7 Young’s Double-Slit Experiment Bright Fringes: Constructive interference Dark Fringes: Destructive interference

8 Two In-Phase Sources: Geometry

9 Interference for Two Sources in Phase Constructive: Destructive:

10 Intensity Distribution What is intensity of two waves out of phase? Average Intensity: Use

11 Average Intensity Average intensity:

12 Diffraction

13 Diffraction Diffraction: The bending of waves as they pass by certain obstacles No spreading after passing though slits Spreading after passing though slits No Diffraction Diffraction

14 Single-Slit Diffraction Destructive interference: “Derivation” (Motivation) by Division: Divide slit into two portions: Don’t get confused – this is DESTRUCTIVE! Now divide slit into four portions: Generalization:

15 Intensity Distribution

16 Concept Question: Lower Limit? Using diffraction seems to be a useful technique for measuring the size of small objects. Is there a lower limit for the size of objects that can be measured this way? 1.Yes – and if we used blue light instead of red light we can measure even smaller objects than the ones we measure using red light 2.Yes – and if we used blue light instead of red light we couldn’t even measure objects as small as the ones we measure using red light 3.No

17 Concept Q. Answer: Lower Limit? Once the feature size a is as small as the light wavelength you can’t go to an angle large enough to satisfy the above equation for any m > 0. Blue light has a shorter wavelength than red light, so you can measure smaller sizes using blue light. Answer: 1. we have the condition that There is a lower limit imposed by the condition, namely that

18 Interference & Diffraction Together

19 Two Slits With Finite Width With more than one slit having finite width a, we must consider 1.Diffraction due to the individual slit 2.Interference of waves from different slits

20 Lecture Demonstration: Double Slits with Diffraction

21 Two Slits With Finite Width

22 Interference & Diffraction

23 Con. Q.: Interference & Diffraction The resulting pattern on a screen far away is shown above, with distantly-spaced zeroes of the envelope, as indicated by the length X above, and closely- spaced zeroes of the rapidly varying fringes, as indicated by the length Y above. Which length in the pattern above is due to the finite width a of the apertures? 1. X 2. Y 3. X and Y 4. Neither X nor Y Coherent monochromatic plane waves impinge on two long narrow apertures (width a) that are separated by a distance d with d > a.

24 Concept Q. Ans.: Inter. & Diffraction Answer: 1. The ‘envelope’ length X depends on slit width. You could infer this in two ways. 1)Slit width a < slit separation d. Angles and size scale inversely, so the bigger features come from a. 2)Interference patterns are roughly equal in magnitude while diffraction creates a strong central peak. So the envelope is from diffraction.

25 Worked Problem: Interference In an experiment you shine red laser light (600 nm) at a slide and see the following pattern on a screen placed 1 m away: a) Are you looking at a single slit or at two slits? b) What are the relevant lengths (width, separation if 2 slits)? What is the orientation of the slits? You measure the distance between successive fringes to be 20 mm

26 Solution: Interference (a) Must be two slits a d

27 Solution: Interference At 60 mm…

28 You just observed an interference pattern using a red laser. What if instead you had used a blue laser? In that case the interference maxima you just saw would be Concept Q.: Changing Wavelengths 1.closer together. 2.further apart. 3.came distance apart.

29 Concept Q. Ans.: Changing Colors Blue light is a higher frequency (smaller wavelength) so the angular distance between maxima is smaller for blue light than for red light Answer: 1. Closer Together

30 Experiment 6, Part I: Measure Laser Wavelength

31 Experiment 6, Part II: Interference from a CD Diffraction Grating d = distance between openings

32 From 2 to N Slits

33 Experiment 6, Part II: Diffraction Grating: CD

34 Experiment 6, Part III: Measure Hair Thickness Single hair strand acts as a single slit (Babinet’s Principle)