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Home , Diffraction, Wavefront

interference and

112N the limits of

‘shadow’ of the 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 behave

and is an electromagnetic - 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 R bright fringes y = m m d

1 R 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 - Huygens’s principle

“every point of a can be considered to be a source of secondary that spread out in all directions with a speed equal to the speed of propagation of the wave”

t =0 wavefront source 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

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 )

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 a sin ✓ = sin ✓ = 2 2 4 2

a sin ✓1 = a sin ✓2 =2 ... a sin ✓m = m physics 112N 20 diffraction pattern from a single slit

R 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 R y = m m a

notice that as the slit size decreases, the spreading of light increases

physics 112N 22 a

many slits of equal size, equally spaced

angular distribution of bright fringes d sin ✓ = m

physics 112N 26 diffraction gratings d sin ✓ = m

can be used to separate different 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 ✓ = m

can use to make precision measurements of components

useful for atomic physics ...

physics 112N 29 a diffraction grating spectrometer d sin ✓ = m 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 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 ✓ = m 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 ✓ = m 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 ✓ = m

physics 112N 35 diffraction from a circular

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