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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

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

• 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.

Why are sunsets orange and red?

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

New velocity can be related to c also lags.

using the refractive index ()

 is wavelength and temperature dependent

In glass  increases as  decreases

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.

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

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

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

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