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Unformatted text preview: PHYSICS 222
Introduction to Classical Physics II
Prof. Ruslan Prozorov
Iowa State University
Fall 2011 LECTURES 31
Dispersion. Interference.
Young’s experiment. what defines a color?
So the atom oscillates with the frequency of the radiation
and then reemits. Frequency remains the same Wavelength changes n1 v1
c
1 f n1f n2 < n1 v2
c
2 1
f n2f “Color” correspond to a fixed frequency. The wavelength
depends on the medium.
PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 2 Dispersion
Light refraction is
wavelength
dependent. This
effect is made more
pronounced if the
index of refraction is
higher. PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 3 example: Dispersion
White light shone into a prism
Dispersion: Different frequencies of color have different indexes of refraction in
glass.
n(f) A. nred > nblue
B. nred < nblue
C. Insufficient info Blue rays bend further from original
direction than red rays
nblue is further from 1 than nred. PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 4 This might be easier to understand (with one refraction only): Blue rays bend further from original direction than red rays
nblue is further from 1 than nred.
PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 5 a famous example of light dispersion PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 6 dispersion and rainbows
The red comes
from the higher
droplets and the
blue from the
lower (as we
have seen in the
wavelength
dependence of
light refraction). PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 7 Huygens’s Principle
o From the work of Christian Huygens in 1678, the geometrical
analysis reveals that every point of a wave front can be
considered to be a source of secondary wavelets that spread
with a speed equal to the speed of propagation of the wave. PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 8 Huygen’s law
All points on a wavefront serve as point sources of secondary wavelets in this example
spherical wavefronts
add up to straight wavefront PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 9 Huygens’s Principle II
o Huygens’s work
can form an
explanation of
reflection and
refraction. PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 10 Law of reflection (from Huygen’s)
Wavefront at t1 Reflected
wavefront
at t4 c 3Δt c 3Δt t2 =t1 +Δt
t3 =t1 +2Δt
t4 =t1 +3Δt Isosceles triangle angles must
be the same PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 11 Law of refraction (from Huygens)
Wavefront at t1 θ1
n1
n2 θ1
θ2 θ2 Refracted
wavefront at t4
θ1 v2t t2 =t1 +Δt
t3 =t1 +2Δt
t4 =t1 +3Δt v1t
θ2 PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University v1t
v2t sin 1 sin 2 sin 2 v2 n1 sin 1 v1 n2
7 November 2011 12 Fermat’s principle
Light will take the path that takes the least time.
A θi B
θr Several paths from A to B
going through mirror surface The shortest path for reflection is the path where θi = θr Similarly for refraction, the shortest path is the one that
satisfies Snell’s law! PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 13 interference
Interference works like for any wave: at any given point, the E/B field is
the vector sum of the E/B field from each wave. Constructive
In phase (or out of
phase by whole λ) Destructive
Out of phase by λ/2 PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 14 path difference ΔL
At point P:
P r2 Constructive interference
L r1 r2 m S2 r1
S1 m 0, 1, 2... Destructive interference 1
L r1 r2 m
2 m 0, 1, 2... Two monochromatic
coherent light sources PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 15 Coherence
S1 and S2 are two sources of monochromatic, coherent light. The phase difference between
these two sources is constant.
Light is produced by millions of atoms emitting at the same
time, with random phases
two light sources are in general
incoherent
Easy trick to produce coherent light: split a beam in two. PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 16 Young’s experiment
Light and dark
alternating fringes r2
Monochromatic
light r1 Max:
L r1 r2 m m 0, 1, 2... •
•
• Waves start off in phase at two slits
Travel different distances to screen
Relative phase at screen PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 17 Dark
Bright
Dark
Bright
Dark Dark
Bright PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 18 PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 19 Position of maxima/minima
R d
Parallel if R >> d L d sin
Bright fringes: d sin m m 0, 1, 2... Dark fringes: 1
2 d sin m PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University m 0, 1, 2... 7 November 2011 20 Intensity for two slit interference
If R >> d, the E fields of each ray are parallel at point P
R Time dependence of
E field at point P : E1 E 0 cos t E2 E 0 cos t with k L k r2 r1 E total 2E 0 cos cos t E max cos cos t
2
2 Amplitude for
resultant wave Intensity I E 2
max IP Imax cos 2
2 PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University Imax = intensity at θ = 0, where phase difference
is ϕ = 0
7 November 2011 21 IP Imax cos 2
2 All maxima should have the same intensity.
But this is what is observed… This is a diffraction effect.
Back to this in a couple of lectures.
PHYS222  Lecture 31  Prof. Ruslan Prozorov  Iowa State University 7 November 2011 22 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.
 Fall '09
 MEYER

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