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Transcript
PH 103 Dr. Cecilia Vogel Lecture 17 Review Lenses ray diagrams application to camera, eye, and corrective lenses more thin lens equation Outline Lenses application to magnifier, microscope angular size and magnification Angular magnification General: M = N/ do What’s the best (biggest) you can do? Put the image at your nearpoint, di=-N, do=Nf/N+f Example Maximum angular magnification f = 2.5 cm Mmax = 1+N/f Mrelax = N/f =10 Mmax = 1+N/f What’s the easiest on the eye? Put the image very far away, di=-, do=f Relaxed-eye angular magnification Mrelax = N/f = 11 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 Telescope Eyepiece lens acts like magnifier Meye = N/do N/feye Lenses subject to chromatic aberration Different colors focus differently Many telescopes are reflecting telescopes to avoid this 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“ 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 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!! 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 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 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 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 Single Slit diffraction pattern Dark Fringes occur at (m =integer again) W sin q m So, width of center bright spot, qcenter q center sin How does pattern depend on 2 W slit width narrower slit causes more diffraction & wider pattern wavelength longer wavelengths diffract more Circular opening diffraction pattern Circular diffraction pattern depends on Aperture radius, a smaller - more diffraction & wider pattern wavelength longer wavelengths diffract more q center 1.22 2 a So two objects separated by ½ that can be resolved as separate bright spots = “Rayleigh Criterion” 1.22 q Rayleigh a