physics 112N

interference and diffraction

physics 112N 2

the limits of ray optics

‘shadow’ of the point of a pin

physics 112N 3

the limits of ray optics

physics 112N 4

the limits of ray optics

physics 112N 5

this is how waves behave

and light is an electromagnetic wave - we need to revisit wave properties

physics 112N 6

a simple system - two wave sourcessuppose we have two sources emitting waves in-phase at the same frequency:

S1

S2

physics 112N 7

the double slit experimentobserve a pattern of dark and light regions, “fringes”

physics 112N 8

the double slit experimentobserve a pattern of dark and light regions, “fringes”

ym = m�R

d

see the textbook for a derivation of

bright fringes

dark fringes y0m =�m+ 1

2

� �Rd

d

R

y

physics 112N 12

diffraction

➜ consider this effect seen near sharp edges:

physics 112N 13

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 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”

plane wavefront

wavelet after a small time

plane wavefrontsource

t = 0

t = �t

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”

plane wavefront

wavelet after a small time

plane wavefrontsource

t = 0

t = �t

a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts

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”

plane wavefront

wavelet after a small time

plane wavefrontsource

t = 0

t = �t

a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts

plane 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”

plane wavefront

wavelet after a small time

plane wavefrontsource

t = 0

t = �t

a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts

original wavefrontpropagated wavefront

physics 112N 18

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 19

a single slit as many sourcesput the screen very far away (or use a lens)

physics 112N 20

a single slit as many sourcesput the screen very far away (or use a lens)

destructive interference when

a

2sin ✓ =

�

2

a2

a sin ✓1 = �

a4

destructive interference when

a

4sin ✓ =

�

2

a sin ✓2 = 2�

. . .

. . . a sin ✓m = m�

physics 112N 21

diffraction pattern from a single slit

positions of dark fringes ym = mR�

a

0

y1

y2

y3

the actual intensity distribution

physics 112N 22

diffraction and slit size

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

positions of dark fringes

ym = mR�

a

physics 112N 26

a diffraction grating

many slits of equal size, equally spaced

d sin ✓ = m�

angular distributionof bright fringes

physics 112N 27

diffraction gratingscan be used to separate different wavelengths of light in a mixed beam

d sin ✓ = m�

e.g. a beam of mixed blue and violet light :

physics 112N 28

diffraction gratings

physics 112N 29

a diffraction grating spectrometercan use to make precision measurements of wavelength components

useful for atomic physics ...

d sin ✓ = m�

physics 112N 30

a diffraction grating spectrometerlight 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

d sin ✓ = m�

physics 112N 31

a diffraction grating spectrometerlight 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

d sin ✓ = m�

physics 112N 32

a diffraction grating spectrometerlight 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)

d sin ✓ = m�

physics 112N 35

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 36

diffraction from a circular aperturesuppose 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 37

diffraction from a circular aperturee.g. the ‘hole’ might be the lens of a telescope

physics 112N 38

resolution

so the ability of a telescope to resolve two objects withsmall angular separation is ultimately limited by the sizeof the lens