lecture5 clh class

8/10/2019 Lecture5 Clh Class

1/31

Geometric Optics

1. consider only speed and direction of a ray

2. take laws of reflection and refraction as facts

3. all dimensions in problems are >>

What can happen to a beam of light when it hits

a boundary between two media?


2/31

Eugene Hecht, Optics, Addison-Wesley,

Reading, MA, 1998.

Conservation Law

() + () + () = 1

() = Fraction Absorbed

() = Fraction Reflected

T() = Fraction Transmitted


3/31

Transmission

How is light transmitted through a medium such

as glass, H2O, etc.?


4/31

Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Rayleigh Scattering

Elastic ( does not change)

Random direction of emission

Little energy loss


5/31

Eugene Hecht, Optics, Addison-

Wesley, Reading, MA, 1998.

Spherical Wavelets

Every unobstructed point of a wavefront, at a given instant,

serves as a source of spherical secondary wavelets. The

amplitude of the optical field at any point beyond is the

superposition of all these wavelets.


6/31

What happens to the raysscattered laterally?


Reading, MA, 1998.


7/31

Are you getting the concept?

Why are sunsets orange and red?


8/31


Forward Propagation


9/31

Wavelets constructivelyinterfere in the forward

direction.


Reading, MA, 1998.


10/31


Scattering is Fast but not Infinitely Fast

What effect does this have on the phase of the wave?


11/31

If the secondary wave lags, then

phase of the resultant wave also lags.

If the secondary wave leads, then

phase of the resultant wave also

leads.

velocity > c

velocity < c


Reading, MA, 1998.


12/31

New velocity can be related to c

using the refractive index ()


v

c=

is wavelength andtemperature dependent

In glass increases as

decreases


13/31

What about the energy in the wave?

Remember: E = h

Frequency remains the same

Velocity and wavelength change

Douglas A. Skoog and James J. Leary, Principles of InstrumentalAnalysis, Saunders College Publishing, Fort Worth, 1992.


14/31

Refraction is a consequence of velocity change



15/31

Snells Law of Refraction

Wavefront travels BD in time t

Wavefront travels AE in time t

BD = v1t

AE = v2t

21 v

AE

v

BD=

1

cADsin

1

=

2

cADsin

2

1sin1 = 2sin2

Ingle and Crouch, Spectrochemical Analysis


16/31


Light in a medium with a refractive index of 1.2 strikes a

medium with a refractive index of 2.0 at an angle of 30degrees to the normal. What is the angle of refraction

(measured from the normal)? Sketch a picture of this

situation.


17/31

Reflection

v and do not change


Reading, MA, 1998.


18/31


Law of Specular Reflection

Velocity is constant

=> AC = BD

AD

BDsin 1=

AD

ACsin 3=

ADsin3 = ADsin1

3 = 1

Angle of Incidence = Angle of Reflection


19/31

Fresnel Equations

For monochromatic light hitting a flat surface at 90

Important in determining reflective losses in optical

systems


20/31


() at different interfaces


21/31

Reflective losses quickly become significant



22/31

Antireflective Coatings

Melles Griot Catalogue

= 1 = 1.38 = 1.5

() = 0.025

() = 0.002

Total () = 2.7%

compared to () = 4.0%

without coating


23/31


Film thickness further reduces reflections


24/31


Observed () for MgF2 coated optic


25/31

If incident beam is not at 90 use Fresnels

complete equation

component component



26/31

For an air-glass interface


For unpolarized light, () increases

as 1 increases

component component


27/31


Example of high

() at high 1


28/31


Brewsters Angle

1 where () of polarized lightis zero

=

1

21-p tan

For an air-glass transition p= 58 40


29/31


Suppose light in a quartz crystal (n = 1.55) strikes a boundary

with air (n = 1.00) at a 50-degree angle to the normal. At whatangle does the light emerge?

Why?


30/31


Total Internal Reflection

1sin1 = 2sin2

Snells Law:

If 2

= 90

==1

21-c1 sin

At any 1 c T() 0


31/31

For a glass-air transition c = 42

Eugene Hecht Optics Addison-Wesley Reading MA 1998

lecture5 clh class

Documents