Download wave optics and optical instruments

WAVE OPTICS AND
OPTICAL
INSTRUMENTS
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Understanding how these rainbows are made
and how certain scientific intruments can
determine wavelength is the domain of wave
optics.
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Light can able viewed as either a particle or a
wave.
The three primary topics we examine are:
interference, diffraction and polarization.
The Interference of Light
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Two waves could add together either constructively or
destructively
In constructive interference- the amplitude of the
resultant wave is greater than that of independent
waves
In destructive interference- the resultant amplitude is
less than that of either individual waves
Conditions for interference:
1. The sources must be coherent, which means the
waves they emit must maintain a constant phase with
respect to each other
2. The waves must have identical wavelengths
(monochromatic)
Young’s Double-Slit Experiment
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The light from the two slits produces a visible
pattern on screen consisting of a series of bright
and dark parallel bands called fringes
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The light intensity on the screen at P is the result
of light from both slits
A light from the lower slit, travels further then
the light from the upper slit, the path difference:
δ(=s) = r2-r1 =d sin θ
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Condition for constructive interference (for
bright fringes): δ=d sin θbright =mλ
Condition for destructive interference (for dark
fringes): δ=d sin θdark =(m + ½)λ
m=0, ±1, ±2. . . – order number
m= 0, the first bright fringe at θbright=0 – is called
zeroth-order maximum
 m=±1 – is called first-order maximum
 m=0, the path difference δ=λ/2 – condition of
location of the first dark fringe on either side of the
central (bright maximum)
 m=1 , δ=3λ/2 – condition for the second dark fringe
on either side
 Position of the bright fringes:
ybright=(λL /d) m
 Position of the dark fringes:
ydark=(λL /d)(m+½)
m= 0, ±1, ±2, …
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Interference in thin films
1. An electromagnetic wave traveling from a medium of
index of refraction n1 toward a medium of refraction
n2 undergoes a 180o phase change on reflection when
n2>n1, there is no phase change in the reflected wave if
n2<n1
 The wavelength of light λn in a medium with index of
refraction n is: λn =λ/n
where λ is the wavelength of light in vacuum
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If 2t= λn /2, then rays 1
and 2 recombine in phase
and constructive
interference results
 Condition for constructive
interference in thin films:
2t=(m+½) λn
m= 0, 1, 2, …
2nt=(m+½) λ (1)
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The general equation
for destructoive
interference in thin
films is:
2 n t= m λ (2)
m= 0, 1, 2, …
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Equation (1) and (2) for constructive and
destructive interference are valid when there is
only one phase reversal (when the media above
and below the thin film both have indices of
refraction greater (respectively less) than the film
If the film is placed between two different
media, one of lower refractive index than the
film and one of higher refractive index, equation
(1) and (2) are reversed:
2nt=(m+½) λ – destructive
2 n t= m λ - constructive
Diffraction
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Diffraction
– the
spreading
out of light
from its
initial line of
travel
Single – Slit Diffraction
sin θ dark=m λ/d
m= ±1, ±2, ±3, …
 This equation gives the
values of θ for which the
diffraction pattern has zero
intensity, where a dark fringe
form
The Diffraction Grating
The condition of
maxima in the
interference pattern
at the angle θ is:
d sin θbright =mλ
m=0, 1, 2, …
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Diffraction grating is
use in CD tracking
Polarization of Light Waves
Polarizing by Reflection
θp+90o+θ2=180o
 θ2=90o-θp;
sinθ2=sin(90o-θp)=cosθp
n=sinθ1/sinθ2=sinθp/sinθ2=sinθp/cosθp=tanθp -Brewster’s
Law
θp=θB- Brewster’s angle
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Optical instruments
The Eye
 The Power P of a
lens in diopters is:
 P=1/f
 Ex:
f=+20cm, P=+5
f=-40cm, P= -2.5
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The simple magnifier
Angular magnification m=β/α
tanα=h/25 ; tanβ=h/p
mmax=β/α=(h/p)/(h/25)=1+25/f
If q=∞, than p=f, m=25/f
The Compound Microscope
 The overall magnification of the compound
microscope: m=M1 me=-L/fo(25cm/fe)
M1 lateral magnification (=-q1/p1=-L/fo);
me- angular magnification(=25cm/fe)of the
eyepiece for an object (corresponding to the
image at q1)placed at the focal point
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The Telescope
m= α/β= (h’/fe)/(h’/fo)=fo/fe