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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

• 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?

() + r() + T() = 1

() = Fraction Absorbed

() = Fraction Reflected

T() = Fraction Transmitted

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

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

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

• Elastic ( does not change)

• Random direction of emission

• Little energy loss

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.

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

Why are sunsets orange and red?

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

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

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

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

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 also lags.

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? also lags.

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.

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

Snell’s Law of also lags.Refraction

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? also lags.

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 also lags.

v and  do not change

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

Law of Specular Reflection also lags.

Velocity is constant

=> AC = BD

3 = 1

Angle of Incidence = Angle of Reflection

Ingle and Crouch, Spectrochemical Analysis

Fresnel Equations also lags.

For monochromatic light hitting a flat surface at 90º

Important in determining reflective losses in optical systems

r() also lags. at different interfaces

Ingle and Crouch, Spectrochemical Analysis

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

Antireflective Coatings also lags.

 = 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

Melles Griot Catalogue

Observed also lags.() for MgF2 coated optic

Melles Griot Catalogue

component also lags.

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

 component

Ingle and Crouch, Spectrochemical Analysis

For an air-glass interface also lags.

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

 component

component

Ingle and Crouch, Spectrochemical Analysis

Example of high also lags.

() at high 1

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

also lags.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? also lags.

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: also lags.

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 also lags.c = 42º

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