63131729 geometrical optics

7/28/2019 63131729 Geometrical Optics

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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


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



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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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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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63131729 geometrical optics

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