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CHAPTER  22  -  REFLECTION & REFR= ACTION OF LIGHT
RAY APPROXIM= ATION & HUYGEN’S PRINCIPLE – SECTION 22.6
= <= /td> <= /td> <= /td>
= Geometric Optics treats light in terms of rays that define the<= br>
pro= pagation direction. The propagation direction changes only when
the= light encounters an interface between two different media of
pro= pagation. At the interface reflection and refraction can occur.
Oth= erwise the rays are straight lines. Geometric Optics is also
kno= wn as Ray Optics. Wavelength dependent superposition
(interference a= nd diffraction) effects are ignored.
<= /td> =
= Physical Optics or Wave Optics deals with the wavelength
dep= endent superposition effects such as interference and
diffraction.
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= =
Ele= ctromagnetic radiation of wavelength, λ, frequency, f and phase
spe= ed, v can be described in terms of its waveform type based on
the shape of th= e wavefronts,
Rays
Wavefronts
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Rays
Wavefronts
Plane Waves<= /u> – wavefronts are planes
Spherical Wa= ves – wavefronts are spheres
=
HUYGENS PRINCIP= LE: Every point on a wavefront is a source of
=  secondary spherical wavelets tha= t form the developing wavefronts
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Plane Wave
Propagation
secondary spher= ical wavelets
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTQALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgBF AAkAgAAAAAAAAAJgjB+gy2D7WDwutltnUtrhljzh5nXVdyHnWI6bCpIW99YkPb/rTokhdrtxIDWP 5Afi/UyUGNFJiwpFSWVLKoRIUkepc+r1IXoTnMsmXg5xWuMp+qGi5nT3rE6H4fdtPb8AADs= ------=_NextPart_01CA5646.837DA730 Content-Location: file:///C:/C6F2A672/PHYSICS1112K-WEB-CH22_files/v3_slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Slide 1
=
How= ever the propagation pattern can be affected if the light
encounters obst= acles or apertures. Consider:
<= /td> <= /td>
(1= ) no = obstacle:  new wavefronts are formed so that t= he wave form is
     undisturbed
wavefronts
rays
c
λ
<= /td> <= /td> <= /td>
lig= ht passes straight through,
dir= ection of the  rays is
unc= hanged and the waveform
is = unchanged. A “shadow” may
be produced
a
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(3) aperture wi= th dimensions that are small relative to λ,   a < λ
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Wit= h two such slits in a screen , one can produce the Double Slit interference=
Pattern on a se= cond screen
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<= /td> =
(4)= aperture with dimensions that are somewhat larger than λ:

                a > λ   but  a  >> λ
a
=
NOT= E: BOTH INTERFERENCE AND DIFFRACTION ARE
ASPECTS OF PHYS= ICAL OPTICS NOT RAY OPTICS
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SINGLE SLIT DIF= FRACTION
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=
= SECTIONS 22.2 & 22.3  -  REFLECTION  AND REFRACTION
                     AND THE LAW OF REFRACTION
= <= /td>
Lig= ht is incident from medium 1 onto an interface with medium 2. The
med= ia are distinguished by their indeces of refraction, ni. The speed of
light in medium= 1 is v1; the speed of light in medium 2 is v2.
NOT= E: WE WILL FIND LATER THAT THE SPEED OF LIGHT V AND THE
IND= EX OF REFRACTION, n  ARE DEPENDENT ON FREQUENCY.
medium 1<= br>
θ1
θ1’
n =3D n1
interface=
n =3D n2
medium 2<= br>
<= /td> =
The= plane of incidence  is the
pag= e surface. E and B can have
com= ponents in the plane of
inc= idence and perpendicular
to it
θ2
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normal
medium 1<= br>
θ1
θ1’
n =3D n1
n =3D n2
medium 2<= br>
θ2
= <= /td> <= /td>
= 52;1  -  angle of incidence                        n1=   -  index of refraction of
= 52;1’  -  angle of reflection                                of me= dium 1
= 52;2  -  angle of refraction                         n2 – index of refraction of
                                            =                          medium 2
=
The= index of refraction, n of a medium:
 (1)                 n =3D  c / v
=
whe= re:  v  -  speed of light in the medium
             c  -  speed of light in a vacuum
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normal
medium 1<= br>
θ1
θ1’
n =3D n1
n =3D n2
medium 2<= br>
θ2
(2)                   n1  =3D  c / v1   and<= span style=3D'mso-spacerun:yes'>  n2  =3D  c / v2
<= /td>
Equ= ations (1) and (2) show that as the speed of light decreases,
n increases
=
als= o, obviously, in free space,  v  =3D c  so:
                      n =3D c / c  =3D 1.0
=
in = a dielectric medium where v < c:
                    n =3D c / v  >  1.0
=
FOR= AIR, WE WILL ASSUME THE INDEX OF REFRACTION,  n  =3D  1.0
THIS  IS  OF  COURSE  AN  APPROXIMATION
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normal
medium 1<= br>
θ1
θ1’
n =3D n1
n =3D n2
medium 2<= br>
θ2
<= /td> <= /td> =
It = can be shown that:
(i= ) θ1’  =3D  = θ1,     angle  of reflection equals angle of incidence
(i= i)  n1 sin θ1=   =3D  n2 sin θ2,     SNELL’S  LAW
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n1 s= in θ1  =3D  n2 sin θ2       SNELL’S  LAW
=
Snell’s Law sho= ws:

If  n2 > n1: :=   sin θ2 < sin = 52;1
or  θ2 < θ= 1
Light bends = toward the normal in the medium of higher index
n1
θ1
<= /td>
For= Example: Light incident
from air = into glass
n2 &g= t; n1
θ2
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(high index int= o a lower index)
<= /td>
= HOWEVER – If n1 > n2
    Then since :
sin θ2= > sin θ1
=
Lig= ht bends away from the normal in the medium of lower
index of refrac= tion
θ1
n1
n2 &l= t; n1
θ2
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<= /td> =
EXAMPLE –=
     Light with a phase speed of 2x10= 8 m/s in glass is incident from
air= onto a glass plate at an angle θ1 =3D 30° with the normal to the pla= te
<= /td> <= /td> =
Find= :
(a= ) n2, the index of refraction of the glass
(b= )  θ2, the angle of refraction of the light in the glass
(a)
(b)
n1
θ1
n2 &g= t; n1
θ2  =3D   19.5°
θ2
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<= /td> = <= /td>
= Atmospheric Refraction -  As light from= the Sun (or any extraterrestrial source)
enc= ounters earth’s atmosphere, it undergoes a process of continuous refraction
on = its path to the surface. The index of refraction of the space it travels in<= br>
out= side the atmosphere is 1.0. The index at the top of the atmosphere begins=
to increase.
apparent source<= /font>
source
n0 = =3D 1.0
ns &g= t; 1.0
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WAVELENGTH O= F REFRACTED LIGHT -
= =
     f  -  frequency of  E-M radiation
     λ0 – wavelength = of the radiation in air (~ vacuum)
     λ  -  wavelength of the rad= iation in a medium of index, n
air
medium n<= br>
λ0
λ
v
c
n  =3D  c / v
n  =3D  f λ0 / f λ
c  =3D  f λ0  ;<= span style=3D'mso-spacerun:yes'>   v  =3D  f λ
n =3D λ0 / λ
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SECTION  22.6  DISPERSION
n is a function= of frequency and ,hence, of λ0
<= /td> = <= /td>
EXA= MPLE: Light with red and blue components is incident
fro= m air on glass at an angle, θ1 =3D 45° with the normal. The
ind= ex for the red light in the glass is  nR<= /sub> =3D 1.4 while the
ind= ex for the blue light is nB =3D 1.6 (exaggerated). Find
= 16;θ, the separation angle between the red and blue rays in
the glass.
n1 = =3D 1.0
n2
θ2B
θ2R
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θ1
θ2B
θ2R
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<= /td>
This Chart Shows
The Variation
Of T= he Index
Of Refraction
With Vacuum
Wavelength In
The Visible Part
Of The Spectrum
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