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Lecture

PHYS 1041 Lecture Notes - Angular Resolution, Radian, Point Particle

3 Pages
118 Views
Winter 2014

Department
Physics
Course Code
PHYS 1041
Professor
Dr.David Fleming

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Physics 1041
Notes
April 7th
Light bright fringes:
θλ
sindm
=
Dark spots between the bright spots:
θλ
sin)
2
1
(dm
=+
Single Opening:
even for a single opening, light waves coming through that opening can undergo
interference
this still creates a pattern of bright and dark spots, but less pronounced
the brightest spot is the central spot with less intense spots on either side,
becoming dimmer with order number
Rayleigh criterion:
the 2 peaks are just barely resolvable as distinct objects if the central maximum of
one of the objects corresponds with the minimum of the other
for a rectangular opening, Rayleigh criterion occurs for:
a
λ
θ
=
min
where
min
θ
is
the minimum angle of separation (in radians), λ is the wavelength of the light, and
a is the width of the slit opening
a complete circle has 360 degrees, or 2π radians
1 radian = 360º/2π
for a circular opening, Rayleigh criterion occurs for
D
λ
θ
22.1
min
=
where
min
θ
is
the minimum angle of separation (in radians), λ is the wavelength of the light, and
D is the diameter of the circular opening
also,
L
s
=
θ
when s is the distance between the two objects, and L is the distance
between the objects and the opening
April 9th
Modern Physics:
in 1905, Einstein's early work involved studying light
it was discovered that light has wave-particle duality: it can behave as both
we think of electrons as a point particle with a negative charge, however they are
also capable of behaving like a wave
the wavelength of the wave of matter is equal to
p
h
=
λ
, where h is equal to
Planck's constant, 6.63 x 10-34Js and p is equal to momentum (mass times
velocity)
therefore all matter can behave as a wave; however we do not see them

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Description
Physics 1041 Notes April 7th Light bright fringes:mλ = d sinθ 1 Dark spots between the bright spots: (m + )λ = d sinθ 2 Single Opening: • even for a single opening, light waves coming through that opening can undergo interference • this still creates a pattern of bright and dark spots, but less pronounced • the brightest spot is the central spot with less intense spots on either side, becoming dimmer with order number Rayleigh criterion: • the 2 peaks are just barely resolvable as distinct objects if the central maximum of one of the objects corresponds with the minimum of the other • for a rectangular opening, Rayleigh criterion occurs for: min= λ where θ minis a the minimum angle of separation (in radians), λ is the wavelength of the light, and a is the width of the slit opening • a complete circle has 360 degrees, or 2π radians • 1 radian = 360º/2π λ • for a circular opening, Rayleigh criterion occurs for min= 1.22 D where θ minis the minimum angle of separation (in radians), λ is the wavelength of the light, and D is the diameter of the circular opening s • also, θ = L when s is the distance between the two objects, and L is the distance between the objects and the opening April 9th Modern Physics: • in 1905, Einstein's early work involved studying light • it was discovered that light has wave-particle duality: it can behave as both • we think of electrons as a point particle with a negative charge, however they are also capable of behaving like a wave • the wavelength of the wave of matter is equal to λ = h , where h is equal to p Planck's constant, 6.63 x 10 Js and p is equal to momentum (mass times velocity) • therefore all matter can behave as a wave; however we do not see them • this is because visible objects have such a large mass, that t
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