Interference and Diffraction

$Interference and Diffraction$ interference and diffraction physics 112N the limits of ray optics ‘shadow’ of the point of a pin physics 112N 2 the limits of ray optics physics 112N 3 the limits of ray optics physics 112N 4 this is how waves behave and light is an electromagnetic wave - we need to revisit wave properties physics 112N 5 a simple system - two wave sources suppose we have two sources emitting waves in-phase at the same frequency: S1 S2 physics 112N 6 the double slit experiment observe a pattern of dark and light regions, “fringes” physics 112N 7 the double slit experiment observe a pattern of dark and light regions, “fringes” y d R see the textbook for a derivation of λR bright fringes y = m m d 1 λR dark fringes y0 = m + m 2 d physics 112N 8 diffraction ➜ consider this effect seen near sharp edges: physics 112N 12 diffraction from a single slit ➜ shine monochromatic light onto a thin slit pattern of light and dark fringes ➜ wide central bright fringe ➜ narrower alternating dark and bright fringes ➜ decreasing intensity away from the center physics 112N 13 an aside on wave propagation - Huygens’s principle “every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave” t =0 plane wavefront source wavelet after a small time t = ∆t plane wavefront physics 112N 14 an aside on wave propagation - Huygens’s principle “every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave” t =0 plane wavefront source wavelet after a small time t = ∆t plane wavefront a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts physics 112N 15 an aside on wave propagation - Huygens’s principle “every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave” t =0 plane wavefront source wavelet after a small time t = ∆t plane wavefront a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts plane wavefront physics 112N 16 an aside on wave propagation - Huygens’s principle “every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave” t =0 plane wavefront source wavelet after a small time t = ∆t plane wavefront a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts propagated wavefront original wavefront physics 112N 17 an aside on wave propagation - Huygens’s principle “every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave” time evolution of a plane wavefront physics 112N 18 a single slit as many sources put the screen very far away (or use a lens) physics 112N 19 a single slit as many sources put the screen very far away (or use a lens) a a 4 ... 2 destructive interference destructive interference when when a λ a λ sin ✓ = sin ✓ = 2 2 4 2 a sin ✓1 = λ a sin ✓2 =2λ ... a sin ✓m = mλ physics 112N 20 diffraction pattern from a single slit Rλ positions of dark fringes y = m y m a 3 y2 y1 0 the actual intensity distribution physics 112N 21 diffraction and slit size positions of dark fringes Rλ y = m m a notice that as the slit size decreases, the spreading of light increases physics 112N 22 a diffraction grating many slits of equal size, equally spaced angular distribution of bright fringes d sin ✓ = mλ physics 112N 26 diffraction gratings d sin ✓ = mλ can be used to separate different wavelengths of light in a mixed beam e.g. a beam of mixed blue and violet light : physics 112N 27 diffraction gratings physics 112N 28 a diffraction grating spectrometer d sin ✓ = mλ can use to make precision measurements of wavelength components useful for atomic physics ... physics 112N 29 a diffraction grating spectrometer d sin ✓ = mλ light from an unknown source is shone though a diffraction grating of 800 lines per mm the diffraction pattern is observed through a rotating telescope a bright line is seen in the forward direction and rotating away from there, the next bright line is seen at 25º 25◦ what is the wavelength of the light ? ~ 530 nm physics 112N 30 a diffraction grating spectrometer d sin ✓ = mλ light from an unknown source is shone though a diffraction grating of 800 lines per mm the diffraction pattern is observed through a rotating telescope a bright line is seen in the forward direction and rotating away from there, the next bright line is seen at 25º 25◦ at what angle will we see the next line ? ~ 58º physics 112N 31 a diffraction grating spectrometer d sin ✓ = mλ light from an unknown source is shone though a diffraction grating of 800 lines per mm the diffraction pattern is observed through a rotating telescope a bright line is seen in the forward direction and rotating away from there, the next bright line is seen at 25º 25◦ when we reach 90º, how many lines will we have seen? three (including the central line) physics 112N 32 white light through a diffraction grating notice that the bright fringes for different colors can start to overlap ... ... can you see why this is from the equation ? d sin ✓ = mλ physics 112N 35 diffraction from a circular aperture suppose the hole the light is traveling through is circular rather than a slit ﬁrst dark ring is at an angle satisfying second dark ring is at an angle satisfying physics 112N 36 diffraction from a circular aperture e.g. the ‘hole’ might be the lens of a telescope physics 112N 37 resolution so the ability of a telescope to resolve two objects with small angular separation is ultimately limited by the size of the lens physics 112N 38.

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