Transcript ReflectionRefraction_Nicolausi_1.12.prelim

Reflection and Refraction
A short overview
Plane wave
A plane wave can be written
as follows:
Here A represent the E or B
fields, q=i,r,t and j=x,y,z
So this is a representation of
the waves that is valid i all
three cases, i.e. the
incoming, the reflected
and the transmitted wave

q i ( k q r  wt )
j
A  Re a e
q
j

Boundary conditions
 For a wave moving from one medium
to another medium we have:
 (i)
1E

1
 (ii)
 2E
E E
11
1
11
2

2
Boundary conditions
 (iii)
 (iv)

1

2
B B
1
1
B 
11
1
1
2
B
11
2
Form of E and B fields
 Electric field and Magnetic fields are
of the form;

E  Re E e
q
j
q
oj

i k .r  wt

B  Re B e
q
j
q
oj
q

i k .r  wt
q


Boundary conditions
Direction of the wave
vectors
Optical laws
 All the three waves have the same
frequency
n1 t
k k  k
n2
i
r
………………………….
1
 Combined fields in medium (1) should be
joined to the fields in medium (2)
 Boundary conditions should hold at all
times and at all points so exponential
factors are equal.
Optical laws
 Spatial terms give

r 
t 
k .r  k .r  k .r
i
when z = 0.
 This holds if components are
separately equal.If incident vector is
in x-z plane, wave vector in y is zero.
Optical laws
 The first law is
k   k   k 
i
r
x
t
x

 k i sin  i  k r sin  r  k t sin  t
x
1.0
Optical laws
 Apply equation (1) to this equation (1.0) we get two
results:

i
r
 
n1 sin   n2 sin 
i
t
 the optical laws apply to all waves
 Reflection and Snell's law can in general apply to nonplanar waves incident upon non-planar interface. This
is shown below
Generalisation of the laws
REFLECTION AND REFRACTION
 From boundary condition 2 above
E
 

i
r
t
cos


E
cos


E
cos

............................................(1.1)
oi
or
ot
 From boundary condition(4)
1
1
Eoi  E0r   Eot ..........................................................................(1.2)
1v1
 2 v2
Fresnel Equations
 solve the two equations
R 11 
E0 r
Eoi
n2
cos  i  cos  t
n1
tan  i   t


n2
tan  i   t
i
t
cos   cos 
n1





T 11
E 0t
2 cos  i


n2
E oi
cos  i  cos  t
n1
Continutation
 When  i   t 


2
R 0
 We get
11
n2
tan  
nn
iB
Reflection and refraction

At angle of incidence

iB
 E vector has no component in plane of incidence.
 This makes it possible to get lineally polarized light from
an unplarized beam.

This fact is used in polarized sun glasses, the filter is
oriented in such away that only light that is polarized
vertically is transmitted, hence avoiding glare or
annoying reflections from horizontal surfaces.
Total internal reflection
n2
haven1  n
 If we
point if




i


1
and at some
ic
From Snell’s law we have
1
sin  t  n1 sin  i
t 

2
surface.)
(transmitted ray glazes the
Total internal reflection
sin


ic
i
1

n1


ic
 we have total internal reflection (no
refracted ray at all). This phenomena is
used in light pipes, fibre optics, and
studying micro waves. In this case we have
an evanescent wave which is rapidly
attenuated and transports
END
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