Topics

1. Topics • Transmission grating spectrometer: • Measuring and calculating the angular dispersion. • Understanding resolving power. • Reflection grating spectrometer: • Using a machinist scale to measure the laser wavelength. • The far-field (Fraunhofer) diffraction pattern of randomly placed identical particles: • Measuring the particle size from the diffraction pattern.

2. Transmission Grating – Normal Incidence Qm a Qm B A What determines whether m=positive is above the dashed line or below the dashed line?

3. Transmission Grating – Oblique Incidence Qm D C Qm B Qi A Qi a Our convention: ccw angles are positive; cw angles are negative. In the example above: both Qi and Qm are positive.

4. Angular Dispersion Different colors (wavelengths) of light have their maxima at slightly different transmitted angles given a particular transmission grating and incident angle. (White light gets “broken up” into rainbow colors at the maxima for m  0. The m = 0 maximum remains white.) Angular dispersion quantifies the change in the (transmitted) angle at which the maxima occur per unit wavelength change:

5. Calculating the Angular Dispersion

6. Resolving Power Under which conditions can you resolve the sodium doublet? Hint: You are given l and Dl. You can make a (numerical) statement involving N, a, Qm and Qi.

7. VIII.A Measurement of Angular Dispersion with White Light Source Diffraction Grating Lens (48mm) Lens (138mm) Screen White Light Source 138mm 48mm • Look at “green” light to get some average wavelength. • Measure DQ from red to blue (Dl 400nm). • Calculate the angular dispersion.

8. VIII.A Measurements with the Helium-Neon Laser m=2 m=1 Laser m=0 m=-1 m=-2 Screen What happens as the grating is rotated? How do the maxima move? Do they? View from top ? Laser Screen

9. VIII.A Wavelength Measurements using Qi=0 and Qi=30 Know what you measure when doing the 30 incident angle measurement! An example: m=+1 View from top Qm=+1 Qi gm=+1 m=0 Laser Qi Qm=-1 gm=-1 m=-1 Screen

10. Once you have figure out what Qm=-1 and Qm=-1 are, you can calculate the wavelength as follows: (Subtract the first equation from the second on each side)

11. Reflection Grating Normal Incidence A Laser B Convention: ccw angles are positive; cw angles are negative. In this example: Qm is negative  m negative Qm Qm

12. Reflection Grating Normal Incidence m=2 m=1 Laser m=0 m=-1 m=-2

13. Reflection Grating Oblique Incidence Laser Qi A B Convention: ccw angles are positive; cw angles are negative. In this example: Qi is positive Qm is negative. D Qm C

14. Reflection Grating Oblique Incidence Laser Qi Qm m=0

15. Reflection Grating Oblique Incidence Laser m=2 m=1 m=0 m=-1 m=-2

16. Let’s rotate the picture to see what we do in VIII.B Screen xm m=2 m=1 m=0 Laser xo a Machinist Scale xo L d

17. Evaluation of Wavelength Get wavelength from slope

18. Machinist Scale: The “grid” spacing d depends on where the laser hits the scale! Example: d

19. Another example: d An example of how not to do it: d=?

20. VIII.C Measuring the Size and Shape of Randomly Distributed Small Particles Look at single slit pattern first. What effect does moving the slit left or right have on the far-field diffraction pattern?

21. Imagine randomly placed slits of the same width: Just as we found with the double slit pattern: We would see an intensity variation in the far field diffraction pattern due to each slit (a single slit pattern). What about the diffraction pattern due to the interaction between the slits (like the double slit pattern for a double slit, or the diffraction grating pattern with regularly placed slits)?

22. VIII.C Measuring the Size and Shape of Randomly Distributed Small Particles For identical particles ,the diffraction pattern from each individual object will look the same in the far field. How about the pattern due to the interaction between the objects? What if the objects were regularly spaced in a pattern?