Diffraction Part 2 Thin film interference with herring (Friday homework !) Butterfly pigmentation Today: Lots of clicker questions on diffraction. Goal: build your intuition and understanding on this topic. How does this work ? (35.5)

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 ……

Is the width of the central bright region Q5.1 This is the diffraction pattern produced by passing light through a single slit of width = a. Is the width of the central bright region greater than a smaller than a equal to a equal to the wavelength of light Greater than A (physical optics) 3

Is the width of the central bright region Q5.1 This is the diffraction pattern produced by passing light through a single slit of width = a. Is the width of the central bright region greater than a smaller than a equal to a equal to the wavelength of light Greater than A (physical optics) Greater than A (physical optics) 4

Q5.2 This is the diffraction pattern produced by passing light through a single slit of width = a If we decrease the slit width, what would happen to the width of the central bright region? Increase Decrease 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. Relate the spreading to the Uncertainty Principle. Theta_1 = lambda/a 5

Q5.2 This is the diffraction pattern produced by passing light through a single slit of width = a If we decrease the slit width, what would happen to the width of the central bright region? Increase Decrease 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. Relate the spreading to the Uncertainty Principle. Theta_1 = lambda/a 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

Q5.3 This is the diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. 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. 7

Q5.3 This is the diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. 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. 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

What is the path difference equal to? Same diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. 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

What is the path difference equal to? Same diffraction pattern produced by passing light with wavelength= l through a single slit of width = a. 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

Given: The wavelength of light =0.0005mm. What is the slit width? 32mm Q5.5 Given: The wavelength of light =0.0005mm. What is the slit width? 32mm 16mm 0.51mm 0.19mm a= 6m(0.0005mm)/16mm=0.19mmD 11

Given: The wavelength of light =0.0005mm. What is the slit width? 32mm Q5.5 Given: The wavelength of light =0.0005mm. What is the slit width? 32mm 16mm 0.51mm 0.19mm a= 6m(0.0005mm)/16mm=0.19mmD a = 6m(0.0005mm)/16mm = 0.19mm 12

Warning: two-slit interference vs single slit diffraction Ch 35: Two slit interference bright fringes N.B. that this equation Ch 36 is for single slit diffraction dark fringes (no m=0 dark fringe) The variables ym have different meanings ! In the first case R is the distance to the screen, x in the 2nd 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 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 ? Narrower Wider No change If the slit becomes narrow, what happens to the peak ? 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 ? Narrower Wider No change If the slit becomes narrow, what happens to the peak ? 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 ? If the slit becomes narrow, what happens to the peak ? Remember this for the discussion of the Heisenberg uncertainty principle in QM Ans: The central peak becomes narrower 19

Example of a single-slit pattern Example (a) The intensity at the center of a single-slit diffraction pattern is I0. 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 I0. 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 I0. 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 I0. 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 Expected to read the book in advance versus