Geometric Optics
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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

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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

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

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


Law of Specular Reflection

Velocity is constant

=> AC = BD

ADsin3 = ADsin1

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:

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

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


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