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

  • 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?


Geometric optics consider only speed and direction of a ray

Conservation Law

() + r() + T() = 1

() = Fraction Absorbed

() = Fraction Reflected

T() = Fraction Transmitted

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


Geometric optics consider only speed and direction of a ray

Transmission

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


Geometric optics consider only speed and direction of a ray

Rayleigh Scattering

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

  • Elastic ( does not change)

  • Random direction of emission

  • Little energy loss


Geometric optics consider only speed and direction of a ray

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.


Geometric optics consider only speed and direction of a ray

What happens to the rays scattered laterally?

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


Geometric optics consider only speed and direction of a ray

Are you getting the concept?

Why are sunsets orange and red?


Geometric optics consider only speed and direction of a ray

Forward Propagation

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


Geometric optics consider only speed and direction of a ray

Wavelets constructively interfere in the forward direction.

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


Geometric optics consider only speed and direction of a ray

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?


Geometric optics consider only speed and direction of a ray

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.


Geometric optics consider only speed and direction of a ray

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.


Geometric optics consider only speed and direction of a ray

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.


Geometric optics consider only speed and direction of a ray

Refraction is a consequence of velocity change

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


Geometric optics consider only speed and direction of a ray

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


Geometric optics consider only speed and direction of a ray

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.


Geometric optics consider only speed and direction of a ray

Reflection

v and  do not change

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


Geometric optics consider only speed and direction of a ray

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


Geometric optics consider only speed and direction of a ray

Fresnel Equations

For monochromatic light hitting a flat surface at 90º

Important in determining reflective losses in optical systems


Geometric optics consider only speed and direction of a ray

r() at different interfaces

Ingle and Crouch, Spectrochemical Analysis


Geometric optics consider only speed and direction of a ray

Reflective losses quickly become significant

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


Geometric optics consider only speed and direction of a ray

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


Geometric optics consider only speed and direction of a ray

Film thickness further reduces reflections

Melles Griot Catalogue


Geometric optics consider only speed and direction of a ray

Observed () for MgF2 coated optic

Melles Griot Catalogue


Geometric optics consider only speed and direction of a ray

component

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

 component

Ingle and Crouch, Spectrochemical Analysis


Geometric optics consider only speed and direction of a ray

For an air-glass interface

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

 component

component

Ingle and Crouch, Spectrochemical Analysis


Geometric optics consider only speed and direction of a ray

Example of high

() at high 1

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


Geometric optics consider only speed and direction of a ray

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

Brewster’s Angle

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

Ingle and Crouch, Spectrochemical Analysis


Geometric optics consider only speed and direction of a ray

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?


Geometric optics consider only speed and direction of a ray

Snell’s Law:

1sin1 = 2sin2

At any 1 c T()  0

Total Internal Reflection

If 2 = 90º

Ingle and Crouch, Spectrochemical Analysis


Geometric optics consider only speed and direction of a ray

For a glass-air transition c = 42º

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


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