Geometric Optics consider only speed and direction of a ray

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. 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 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 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

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. 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  = 1.5  = 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

23. Film thickness further reduces reflections Melles Griot Catalogue

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

25. component If incident beam is not at 90º use Fresnel’s complete equation  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. 1 where () of polarized light is zero Brewster’s Angle 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. Snell’s Law: 1sin1 = 2sin2 At any 1 c T()  0 Total Internal Reflection If 2 = 90º Ingle and Crouch, Spectrochemical Analysis

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