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