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 x, 2 nm ,000, 10 nm (3-d)

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

5. What determines (ultimate, i. e
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?
Δpx Δx ≥ h/2π Δx = resolution; how small spot
Remember: Applies to each direction!
Photon 1: p = p ŷ
Photon 2: px = p sin θ : py = p cos θ
Δpx =
p sin θ – (- p sin θ)
= 2p sin θ
Δx = resolution

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

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

11. Wavelength & Resolution
visible=≈ nm
/2 N.A.: air= l/2: oil= l/(2)(1.4)
= 500 nm: Best resolution nm
red
green
blue
purple
400 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?
Relationship between radiation of an object and its temperature
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

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

14. Accuracy vs. Resolution
What’s the difference?
Point-object:
Accuracy is how well you can tell where it is.
Resolution is how well you can tell two identical objects apart
Unlimited accuracy
Crater Lake
W.E. Moerner
center
width
Enough photons
(w/photons1/2)
Center determined to ~ 1.3 nm
1-500 msec
250 nm
lin
lout
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. Answer, and turn in at the end of class.
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.