1. PH 103 Dr. Cecilia Vogel Lecture 17

2. Review Outline  Lenses  application to magnifier, microscope  angular size and magnification  Lenses  ray diagrams  application to camera, eye, and corrective lenses  more thin lens equation

3. Angular magnification  What’s the best (biggest) you can do?  Put the image at your nearpoint, d i =-N, d o =Nf/N+f  Maximum angular magnification  M max = 1+N/f  What’s the easiest on the eye?  Put the image very far away, d i =- , d o =f  Relaxed-eye angular magnification  M relax = N/f General: M = N/ d o Example f = 2.5 cm M max = 1+N/f = 11 M relax = N/f =10

4. Telescope  Two lenses -- can do more than cases I-IV  Type of lens:  two converging lenses  objective lens is nearer object  eyepiece (or ocular) lens is near eye  Objective lens  object far away  So farther than focal point  so image is real, inverted Java applet Java applet

5. Telescope  Eyepiece lens acts like magnifier  M eye = N/d o  N  f eye  Lenses subject to chromatic aberration  Different colors focus differently  Many telescopes are reflecting telescopes to avoid this

6. Recall Ray Model  Light travels in a straight line  except when it strikes a new material  Works very well for all waves when wavelength << sizes of obstacles and openings  Examples  light through a window or open door  satellite signal approaching earth  “line-of-sight“

7. Diffraction  Ray model breaks down for all waves when wavelength  size of obstacles/openings  Wave diffracts through opening, or around obstacle  Examples  sound through open door  radio wave around building  light thru very small slit  not line-of-sight

8. Interference  If two hoses spray water at a wall, twice as much water. 1+1=2  If two waves strike a wall, add wave functions. 1+1=0 thru 4!!

9. Constructive Interference  Occurs when crest meets crest and trough meets trough: “in phase”  Overall intensity (brightness) is four times as bright as a single wave

10. Destructive Interference  Occurs when crest meets trough: “out of phase”  Overall intensity (brightness) is 0!  Also, can have anything between fully constructive and fully destructive. Can have anything from 0 to 4 times as bright

11. Coherence  Do you see interference between two light bulbs?  No!  Light in bulb is produced by many atoms  each atom doing its own thing  phase changes randomly and rapidly  Waves go in and out of phase -- bright to dark -- faster than we can observe

12. Coherence  How do you get two waves that are coherent?  Take one source, split it, bring it back together Examples:  light passing through two (or more) slits  light passing around opposite sides of obstacle  light reflecting from top and bottom surface of thin film  light passing through and reflecting from a partially-silvered mirror

13. Single Slit diffraction pattern  Dark Fringes occur at (m =integer again)  So, width of center bright spot,  center  How does pattern depend on  slit width  narrower slit causes more diffraction & wider pattern  wavelength  longer wavelengths diffract more

14. Circular opening diffraction pattern  Circular diffraction pattern depends on  Aperture radius, a  smaller - more diffraction & wider pattern  wavelength  longer wavelengths diffract more  So two objects separated by ½ that can be resolved as separate bright spots = “Rayleigh Criterion”