 # 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?

() = Fraction Absorbed () = Fraction Reflected
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 Elastic ( does not change)
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?

Are you getting the concept?
Why are sunsets orange and red?

Wavelets constructively interfere in the forward direction.

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

Snell’s Law of 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?
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

3 = 1 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

Antireflective Coatings
 = 1  = 1.38  = 1.5 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

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

Brewster’s Angle 1 where () of polarized light is zero
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?

Total Internal Reflection
1sin1 = 2sin2 Snell’s Law: If 2 = 90º At any 1  c T()  0 If light goes from a high-index material into a low-index material at a steep angle, something unexpected happens. In this case, the light cannot escape into the air. It is all reflected back into the quartz in a phenomenon known as total internal reflection (key for fiber optics). Ingle and Crouch, Spectrochemical Analysis

For a glass-air transition c = 42º