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# Geometric Optics consider only speed and direction of a ray - PowerPoint PPT Presentation

Geometric Optics consider only speed and direction of a ray take laws of reflection and refraction as facts all dimensions in problems are >> l What can happen to a beam of light when it hits a boundary between two media?. Conservation Law. () + r() + T() = 1

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Geometric Optics consider only speed and direction of a ray

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#### Presentation Transcript

• Geometric Optics

• consider only speed and direction of a ray

• take laws of reflection and refraction as facts

• all dimensions in problems are >> l

• What can happen to a beam of light when it hits a boundary between two media?

Conservation Law

() + r() + T() = 1

() = Fraction Absorbed

() = Fraction Reflected

T() = Fraction Transmitted

Transmission

How is light transmitted through a medium such as glass, H2O, etc.?

Rayleigh Scattering

• Elastic ( does not change)

• Random direction of emission

• Little energy loss

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.

What happens to the rays scattered laterally?

Are you getting the concept?

Why are sunsets orange and red?

Forward Propagation

Wavelets constructively interfere in the forward direction.

Scattering is Fast but not Infinitely Fast

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

If the secondary wave lags, then phase of the resultant wave also lags.

velocity < c

If the secondary wave leads, then phase of the resultant wave also leads.

velocity > c

New velocity can be related to c

using the refractive index ()

 is wavelength and temperature dependent

In glass  increases as  decreases

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 Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.

Refraction is a consequence of velocity change

Snell’s Law ofRefraction

Wavefront travels BD in time t

BD = v1t

Wavefront travels AE in time t

AE = v2t

1sin1 = 2sin2

Ingle and Crouch, Spectrochemical Analysis

Are you getting the concept?

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 30

degrees to the normal. What is the angle of refraction

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

situation.

Reflection

v and  do not change

Law of Specular Reflection

Velocity is constant

=> AC = BD

3 = 1

Angle of Incidence = Angle of Reflection

Ingle and Crouch, Spectrochemical Analysis

Fresnel Equations

For monochromatic light hitting a flat surface at 90º

Important in determining reflective losses in optical systems

r() at different interfaces

Ingle and Crouch, Spectrochemical Analysis

Reflective losses quickly become significant

Antireflective Coatings

 = 1.5

 = 1

 = 1.38

r(l) = 0.002

r(l) = 0.025

Total () = 2.7%

compared to r(l) = 4.0%

without coating

Melles Griot Catalogue

Film thickness further reduces reflections

Melles Griot Catalogue

Observed () for MgF2 coated optic

Melles Griot Catalogue

component

If incident beam is not at 90º use Fresnel’s complete equation

 component

Ingle and Crouch, Spectrochemical Analysis

For an air-glass interface

For unpolarized light, () increases as 1 increases

 component

component

Ingle and Crouch, Spectrochemical Analysis

Example of high

() at high 1

1 where () of polarized light is zero

Brewster’s Angle

For an air-glass transition p = 58° 40’

Ingle and Crouch, Spectrochemical Analysis

Are you getting the concept?

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 what

angle does the light emerge?

Why?

Snell’s Law:

1sin1 = 2sin2

At any 1 c T()  0

Total Internal Reflection

If 2 = 90º

Ingle and Crouch, Spectrochemical Analysis

For a glass-air transition c = 42º