Diffraction Part 2 Thin film interference with herring

Diffraction Part 2 Thin film interference with herring (Friday homework !) Today: Lots of clicker questions on diffraction. Goal: build your intuition and understanding on this topic. Butterfly pigmentation How does this work ? (35. 5) 1

Around the corner Physics demon Question: Can you see around a corner ? Can you hear around a corner ? Explain why ? Sound wavelengths are of order 1 m, in contrast to ……

Q 5. 1 This is the diffraction pattern produced by passing light through a single slit of width = a. Q. Is the width of the central bright region A. B. C. D. greater than a smaller than a equal to the wavelength of light 3

Q 5. 1 This is the diffraction pattern produced by passing light through a single slit of width = a. Q. Is the width of the central bright region A. B. C. D. greater than a smaller than a equal to the wavelength of light Greater than A (physical optics) 4

Q 5. 2 This is the diffraction pattern produced by passing light through a single slit of width = a Q. If we decrease the slit width, what would happen to the width of the central bright region? A. Increase B. Decrease C. Stay the same 5

Q 5. 2 This is the diffraction pattern produced by passing light through a single slit of width = a Q. If we decrease the slit width, what would happen to the width of the central bright region? A. Increase B. Decrease C. Stay the same If the slit is very, very narrow, then we have a “point” source which the wave spreads uniformly => width of bright region increases but intensity decreases. 6

Q 5. 3 This is the diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. Q. Consider the paths from the top and bottom edges of the slit to the first dark region (m=1). What is the path difference equal to? A) λ/ 2 B) λ C) 3/2 λ D) 2 λ 7

Q 5. 3 This is the diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. Q. Consider the paths from the top and bottom edges of the slit to the first dark region (m=1). What is the path difference equal to? A) λ /2 B) λ C) 3/2 λ D) 2 λ B) lambda/2 for a dark fringe. Top and middle lambda/2 out of phase and middle and bottom lambda/2 out of phase. a is λ, a/2 is λ /2 8

Q 5. 4 Same diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. Q. Consider the paths from the top and a/2 position (middle of the slit) to the second dark region (m=2). What is the path difference equal to? A) λ /2 B) λ C) 3/2 λ D) 2 λ 9

Q 5. 4 Same diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. Q. Consider the paths from the top and a/2 position (middle of the slit) to the second dark region (m=2). What is the path difference equal to? A) λ /2 B) λ C) 3/2 λ D) 2 λ 10

Q 5. 5 Given: The wavelength of light =0. 0005 mm. What is the slit width? A. B. C. D. 32 mm 16 mm 0. 51 mm 0. 19 mm 11

Q 5. 5 Given: The wavelength of light =0. 0005 mm. What is the slit width? A. B. C. D. 32 mm 16 mm 0. 51 mm 0. 19 mm a = 6 m(0. 0005 mm)/16 mm = 0. 19 mm 12

Warning: two-slit interference vs single slit diffraction Ch 35: Two slit interference bright fringes The variables ym have different meanings ! N. B. that this equation Ch 36 is for single slit diffraction dark fringes (no m=0 dark fringe) In the first case R is the distance to the screen, x in the 2 nd case 13

Review: Intensity in the single-slit diffraction pattern What is β ? The angle θ is between P and a line normal to the middle of the slit Intensity of a single slit diffraction pattern 14

Review: Intensity maxima in a single-slit pattern • The figure on the right shows the intensity versus angle in a single-slit diffraction pattern. • The minima occur when β is a multiple of 2π, i. e. at • The location of the maxima are found by taking the derivative of and setting it to zero. Surprisingly, these are not precisely where • In fact, there are no maxima for m = 0 in this expression. The central maximum is wider than the others, and occurs at θ = 0. • Using these approximate values of β in the intensity, we find 15

Another way to think about this a b Imagine P is a minimum: condition is λ/2 for a/2 spacing But what about points a and b ? 16

Width of the single-slit pattern • The width of the single-slit diffraction pattern depends on the ratio of the slit width a to the wavelength λ. If the slit becomes wider, what happens to the central peak ? a) Narrower b) Wider c) No change 17

Width of the single-slit pattern • The width of the single-slit diffraction pattern depends on the ratio of the slit width a to the wavelength λ. If the slit becomes wider, what happens to the central peak ? a) Narrower b) Wider c) No change 18

Width of the single-slit pattern • The width of the single-slit diffraction pattern depends on the ratio of the slit width a to the wavelength λ. If the slit becomes wider, what happens to the central peak ? Ans: The central peak becomes narrower Remember this for the discussion of the Heisenberg uncertainty principle in QM 19

Example of a single-slit pattern • Example (a) The intensity at the center of a single-slit diffraction pattern is I 0. What is the intensity at a point in the pattern where there is a 66 -radian phase difference between wavelets from the two edges of the slit? (b) If this point is 7 degrees from the central maximum, how many wavelengths across is the slit? What do we need to know to work this problem? Remember to work in radians not degrees 20

Example of a single-slit pattern • Example (a) The intensity at the center of a single-slit diffraction pattern is I 0. What is the intensity at a point in the pattern where there is a 66 -radian phase difference between wavelets from the two edges of the slit? (b) If this point is 7 degrees from the central maximum, how many wavelengths across is the slit? So what is the 66 -radian phase difference ? So what expression do we need ? Remember to work in radians not degrees 21

Example of a single-slit pattern • Example (a) The intensity at the center of a single-slit diffraction pattern is I 0. What is the intensity at a point in the pattern where there is a 66 -radian phase difference between wavelets from the two edges of the slit? (b) If this point is 7 degrees from the central maximum, how many wavelengths across is the slit? • (a) • (b) For part b what do we need to know ? Remember to work in radians not degrees 22

Example of a single-slit pattern • Example (a) The intensity at the center of a single-slit diffraction pattern is I 0. What is the intensity at a point in the pattern where there is a 66 -radian phase difference between wavelets from the two edges of the slit? (b) If this point is 7 degrees from the central maximum, how many wavelengths across is the slit? • (a) • (b) Remember to work in radians not degrees 23

Two slits of finite width So we have double narrow slit interference (Ch 35), single slit diffraction (Ch 36) and now two finite width slits (Ch 36). How do we treat this? 24

Two slits of finite width • The overall pattern of two finite-width slits is the product of the two patterns, i. e. So we have double narrow slit interference (Ch 35), single slit diffraction (Ch 36) and now two finite width slits (Ch 36). 25

Two slits of finite width • The overall pattern of two finite-width slits is the product of the two patterns, i. e. Reminder So we have double narrow slit interference (Ch 35), single slit diffraction (Ch 36) and now two finite width slits (Ch 36). 26

Two slits of finite width (comparison to other cases) • The overall pattern of two finite-width slits is the product of the two patterns, i. e. So we have double narrow slit interference (Ch 35), single slit diffraction (Ch 36) and now two finite width slits (Ch 36). 27

Two slits of finite width (look at this in detail) • The overall pattern of two finite-width slits is the product of the two patterns, i. e. So we have double narrow slit interference (Ch 35), single slit diffraction (Ch 36) and now two finite width slits (Ch 36). 28

Two slits of finite width • The overall pattern of two finite-width slits is the product of the two patterns, i. e. So we have double narrow slit interference (Ch 35), single slit diffraction (Ch 36) and now two finite width slits (Ch 36). 29

For next time • Don’t confuse the following – Meaning of ym in narrow double slit and single wide (diffraction) cases versus • Expected to read the book in advance 30