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Geometric Optics consider only speed and direction of a ray

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- 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

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

Transmission

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

Rayleigh Scattering

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

- 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.

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

What happens to the rays scattered laterally?

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

Are you getting the concept?

Why are sunsets orange and red?

Forward Propagation

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

Wavelets constructively interfere in the forward direction.

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

Scattering is Fast but not Infinitely Fast

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

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

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

New velocity can be related to c

using the refractive index ()

is wavelength and temperature dependent

In glass increases as decreases

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

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

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

Snell’s Law ofRefraction

Wavefront travels BD in time t

BD = v1t

Wavefront travels AE in time t

AE = v2t

1sin1 = 2sin2

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

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

Law of Specular Reflection

Velocity is constant

=> AC = BD

ADsin3 = ADsin1

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

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

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

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

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:

1sin1 = 2sin2

At any 1 c T() 0

Total Internal Reflection

If 2 = 90º

Ingle and Crouch, Spectrochemical Analysis

For a glass-air transition c = 42º

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