1. Prismswww.edmundoptics.com Right AngleEquilateralPentagonalDove

2. More Wave Guiding www.edmundoptics.com

3. Interference and Diffraction

4. Huygens-Fresnel Principle Adapted from: Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998. What if we block some of the wavelets?

5. Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998. Diffraction increases as aperture size  Diffraction increases as aperture size  If is large compared to the aperture, the waves will spread out at large angles into the region beyond the obstruction. Diffraction

6. Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis

7. Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis For Destructive Interference: x = /2 W sin  = W sin  =

8. Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis For Destructive Interference: x = /2 W sin  = 2 W sin  = 2

9. Diffraction Pattern From a Single Slit Ingle and Crouch, Spectrochemical Analysis For Destructive Interference: W sin  = m W sin  = m m = ±1, ±2, ±3, …

10. Ingle and Crouch, Spectrochemical Analysis Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998. W sin  = W sin  = sin   / W More precisely: sin  = 1.22 / W Diffraction Limited Beam Width

11. Airy pattern radius from central peak to 1 st minimum: Diffraction-limited resolution: http://www.microscopyu.com/articles/formulas/formulasresolution.html Diffraction-Limited Resolution

12. Eugene Hecht, Optics, 1998. Diffraction Gratings Plane or convex plate ruled with closely spaced grooves (300- 2400 grooves/mm). http://www.olympusmicro.com/primer/java/imageformation/gratingdiffraction/index.html

13. Two parallel monochromatic rays strike adjacent grooves and are diffracted at the same angle (  ). Difference in optical pathlength is AC + AD. For constructive interference: m = (AC + AD) m = 0,  1,  2,  3, … Ingle and Crouch, Spectrochemical Analysis Grating Equation

14. m = (AC + AD) AC = d sin  AD = d sin  Combine to give Grating Equation: d(sin  + sin  ) = m d(sin  + sin  ) = m Ingle and Crouch, Spectrochemical Analysis Grating Equation Grating Equation only applies if: d > /2

15. Are you getting the concept? At what angle would you collect the 1 st order diffracted light with = 500 nm if a broad spectrum beam is incident on a 600 = 500 nm if a broad spectrum beam is incident on a 600 groove/mm grating at  i = 10 ° ? For = 225 nm? For = 750 nm?

16. Overlapping Orders Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992. d(sin  + sin  ) = m d(sin  + sin  ) = m For Example: 1 st Order = 400 nm 2 nd Order = 200 nm 3 rd Order = 133 nm Any equivalent m combinations will share  values. Calculate the free spectral range:  f = /(m+1)

17. Blaze Angle (  ) Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998. Intensity is highest when  matches the angle of specular reflection.

18. Blaze Angle (  ) Blazed gratings direct most of the light towards a higher order band. Optimum Intensity:  = 2  Blaze Wavelength ( b ): b = dsin2  b = dsin2  Ingle and Crouch, Spectrochemical Analysis Efficiency drops to ~50% at 2/3 b and 3/2 b.

19. Ingle and Crouch, Spectrochemical Analysis Czerny – Turner Monochromator Slits: determine resolution and throughput

20. Can change angle of grating to focus different on the exit slit. Take-off angle (  ) is constant. Change  to direct different towards    =  +   =  -  m = 2 d sin  cos  Ingle and Crouch, Spectrochemical Analysis