Lecture 9 Announcements

1. Lecture 9 Announcements Next Wed. Quiz covering reading– Kinosita & Cross (2 articles) on ATPase Homework due

2. Today Techniques for measuring distances (where physicists have made a big impact on bio.) X-ray diffraction (atomic resolution) Electron (Imaging) Microscopy (nm-scale) Visible (Imaging) Microscopy (nm - µm) Bacteria on head of a pin at different magnifications

3. Microscopes Cells discovered with invention of microscope. MBC, Fig. 4- Or with CCD 1000x, 0.2um 106x, 2 nm 20,000, 10 nm (3-d)

4. A single spot will be smeared out, no matter how small the spot is, because of the wavelength of light to ~ l/2. Point-Spread Function (PSF) Resolution: The Rayleigh criteria How well can you resolve two point objects?

5. What determines (ultimate, i.e. best) resolution of technique… microscope, eye, etc.? [2 parts] 1. Primarily λ (wavelength). Why? Uncertainty principle (Will show). 2. Collection Angle/focal length/ Numerical Aperture Resolution ≈ # λ/N.A. # = a factor = ½ (details not important) Resolution ≈ λ/2N.A.

7. Photon 1 What is uncertainty principle, applied here? ΔpxΔx ≥ h/2πΔx = resolution; how small spot Remember: Applies to each direction! Photon 1: p = p ŷ Photon 2: px = p sin θ : py = p cos θ p sin θ – (- p sin θ) = 2p sin θ Δpx = Δx = resolution

8. Wavelength at screen Calculating resolution DpDx = h/2p 2psinqDx = h/2p p = h/l … need n. Where does n come in?

9. Coverslip (glass) (thin, n= 1.33) object Fill with oil (n ~ 1.5) where air = 1 n in resolution (Homework)

11. 400 nm 488 514 532 633 750 blue green purple red Wavelength & Resolution • visible=≈ 400-700 nm • /2 N.A.: air= l/2: oil= l/(2)(1.4) • = 500 nm: Best resolution 200-250 nm Short l Long l Modern day optical microscopes are highly optimized– perfect diffraction limited. (Electron microscopes are 1000’s of times worse.)

12. Relationship between radiation of an object and its temperature l of electrons (Who was famous guy who got Nobel prize in 1929 for the “wave nature of electrons”? What relationship between wavelength and E, p, does this correspond to? Debroglie E= hn = hc/l; p = h/l Where does Planck’s constant come from? The Planck constant came from law of black body radiation: that the electromagnetic radiation emitted by a black body could be modeled as a set of harmonic oscillators with quantized energy of the form: E = hn http://en.wikipedia.org/wiki/Black-body

13. Resolution of Electron Microscope Given electron 100 KeV, (typical upper-value for electron microscope) what is l? h =6.63 × 10-34 J-sec = 4.1 × 10-15 eV-sec E100kV = 0.004 nm (really short!) In reality, because not perfect electron lenses, resolution is ~1 nm. Far from ideal.

14. center Crater Lake width W.E. Moerner lin Enough photons (w/photons1/2) Center determined to ~ 1.3 nm Accuracy vs. Resolution What’s the difference? Point-object: Accuracyis how well you can tell where it is. Resolution is how well you can tell two identical objects apart Unlimited accuracy 250 nm lout 1-500 msec N ~10,000 photons w ~ 250 nm D ~  1.25 nm What limits, in practice, accuracy? Ans: drift of the stage (other things will be discussed later)

15. Class evaluation • What was the most interesting thing you learned in class today? • 2. What are you confused about? • 3. Related to today’s subject, what would you like to know more about? • 4. Any helpful comments. Answer, and turn in at the end of class.