1. 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?

2. () = Fraction Absorbed () = Fraction Reflected
Conservation Law
() + r() + T() = 1
() = Fraction Absorbed
() = Fraction Reflected
T() = Fraction Transmitted
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

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

4. 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

5. 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.

6. What happens to the rays scattered laterally?
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

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

8. Forward Propagation
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

9. Wavelets constructively interfere in the forward direction.
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

10. 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?

11. 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.

12. 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.

13. 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.

14. Refraction is a consequence of velocity change
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

15. 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

16. 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.

17. Reflection v and  do not change
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

18. 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

19. Fresnel Equations
For monochromatic light hitting a flat surface at 90º
Important in determining reflective losses in optical systems

20. r() at different interfaces
Ingle and Crouch, Spectrochemical Analysis

21. Reflective losses quickly become significant
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

22. 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

23. Film thickness further reduces reflections
Melles Griot Catalogue

24. Observed () for MgF2 coated optic
Melles Griot Catalogue

25. If incident beam is not at 90º use Fresnel’s complete equation
 component
component
Ingle and Crouch, Spectrochemical Analysis

26. For an air-glass interface
For unpolarized light, () increases as 1 increases
 component
component
Ingle and Crouch, Spectrochemical Analysis

27. Example of high () at high 1
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

28. Brewster’s Angle 1 where () of polarized light is zero
For an air-glass transition p = 58° 40’
Ingle and Crouch, Spectrochemical Analysis

29. 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?

30. 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

31. For a glass-air transition c = 42º
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.