63131729 geometrical optics
TRANSCRIPT
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Geometric optics
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Rays
rays point in direction that
light travels
crests occur on wave fronts
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Ray Optics
A light ray can be defined by two co-ordinates:
xin, qin
xout, qout
its position,x
its slope, q
Optical axis
x
q
These parameters will change with distance and as the ray
propagates through optics.
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Light raysradiatefrom a pointobject in alldirections.
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Reflection from aplane mirror.
P is a virtual image.
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Objects and images
Object Image
Rays from point
on object reflect
from mirror
Reflected rays
appear to come
from a point
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Reflection
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Specular reflection
(mirror)Diffuse reflection
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Reflection The angle of incidence equals the angle of reflection
qi = qr , where both angles are measured from the normal:
Note also, that all rays lie in the plane of incidence
qi qr
qi qr x
Eiqi
Erqr
q qi r
Why?
This law is quite general; we supply a limited justification whensurface is a good conductor,
Electric field lines are perpendicular to the conducting surface.
The components of E parallel to the surface of the incident and reflected
wave must cancel!!
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Law of reflection
q q
Planar reflectingsurface (mirror)
q = angle of incidence
q
= angle of reflection
Law of reflection
q'
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Refraction
But it is really here!!
He sees the
fish here.
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Index of Refraction The wave incident on an interface can not only reflect, but it can also
propagate into the second material.
Claim the speed of an electromagnetic wave is different in matter than it is in
vacuum.
Recall, from Maxwells eqns in vacuum:
c 1
0 0
n c
v
How are Maxwells eqns in matter different? 0 , 0 Therefore, the speed of light in matter is related to the speed of light
in vacuum by:
1n0
where n = index of refraction of the material:
The index of refraction is frequency dependent: For example
nblue > nred
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Light inside a medium
Light interacts with particles inside materials
This slows down the light
The speed of light inside a medium is less than cc
v
n
n is called the index of refraction
It is always bigger than 1
Material nAir 1.000
Water 1.333
Glass 1.6
Diamond 2.419
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Law of refraction
q1
q1 = angle of incidence
q2 = angle of refraction
Snells Law
2211sinsin qnn
n1
n2
q2
( n2> n
1in diagram )
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Refraction
Law of Refraction
(Snells Law)
n1sinq1 = n2sinq2
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Refraction
Low to high index, light bends towards the normal line.
High to low index, light bends away from the normal line.
n1 < n2
n1sinq1 = n2sinq2
n1
> n2
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n1
n2
Two simple effects
Object underwater appearsto be at a shallower depth
2
1sin
n
nC
Total internal reflection
qC
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Total Internal Reflection (TIR)
sinqc
= n2
/ n1
Critical Angle
Required:
n1
> n2
q1 > qc
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TIR can only occur if
1. light goes from high index to low index AND
2. angle of incidence is greater than the critical angle
Total Internal Reflection (TIR)
n1
n2 qc
water to air 1.33 1 48.8
glass to air 1.5 1 41.8 glass to water 1.5 1.33 62.5
Examples
Total Internal Reflection (TIR)
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Total Internal Reflection
q1
q2
1 1
22
sin
sin
n
n
q
q What happens if the expression on the right
is bigger than one?
If the expression on the right is one or
bigger, than all the light gets reflected
1
2
sin1 c
n
n
q
2
1
sinc
n
n
q
Called total internal reflection
Total internal reflection occurs only
when light moves into a medium oflower index of refraction
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Total internal reflection, Critical angle
1
2sinn
n
c
1q
n2
n1
> n2
Incidentlight
Transmitted
(refracted) light
Reflectedlight
kt
TIR
Evanescent wave
ki
kr
(a) (b) (c)
Light wave travelling in a more dense medium strikes a less dense medium. Depending on the incidence angle with respect to , which is determined by the ratio of the refractive
indices, the wave may be transmitted (refracted) or reflected. (a) (b) (c)and total internal reflection (TIR).
2
1
c
902
c
1
c
c 1 c 1c
1
Critical angle
1
2sinn
n
c
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A light beam enters on the left in air, and we
want it to be reflected by the block of
glass. Do we have total internal reflection
in this case?A) Yes
B) No
C) Insufficient Information
What if water getsbehind the prism?
Total Internal Reflection
Material n
Air 1.000
Water 1.333
Glass 1.6
Diamond 2.419
2
1
sinc
n
n
q
45o
45o90o
45o
1 12
1
1sin sin 38.71.6
C
n
nq
1 2
1
sinc
n
n
q
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Total Internal Reflection (TIR)
Application: Optical Fiber
clad
core
Optical Cable
Single Fiber
Optical Fiber
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Prisms
downbendsLight
sinsin
21
21
qq
qq
n
downbendsLight
sinsin
43
43
qq
qq
n
q1
q2
Entering
q3q4
Exiting
For air/glass interface, we
use n(air)=1, n(glass)=n
P i
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Prisms
q1
q2
q3q4
Overall Deflection
At both deflections the amount of downward deflection
depends on n (and the prism apex angle, ). Different colors will bend different amounts !
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Dispersion
The amount by which light slows down can
depend on the wavelength of the light
The amount by which the light is bent can
depend on the wavelength of the light1 1 2 2sin sinn nq q
For most materials, short wavelengths (blue)are slowed more than long wavelengths (red)
White light (mixture of all
colors) gets split into its
constituent colors
c
vn
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Refraction & Dispersion
Light is bent and the resultant colors separate (dispersion).
Red is least refracted, violet most refracted.
Short wavelengths are bent
more than long wavelengths
rac
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LIKE SO! In second rainbow
pattern is reversed
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