PH 103

Dr. Cecilia VogelLecture 17

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

Angular magnification

What’s the best (biggest) you can do? Put the image at your nearpoint, di=-N,

do=Nf/N+f Maximum angular magnification

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

General: M = N/ do

Examplef = 2.5 cm

Mmax = 1+N/f

= 11

Mrelax = N/f=10

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

TelescopeEyepiece lens acts like magnifier

Meye = N/do Nfeye

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

InterferenceIf 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 InterferenceOccurs 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 atomseach atom doing its own thingphase changes randomly and rapidlyWaves 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

togetherExamples: 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)

So, width of center bright spot, center

How does pattern depend onslit width

narrower slit causes more diffraction & wider pattern

wavelengthlonger wavelengths diffract more

mW sin

Wcenter

2sin

Circular opening diffraction pattern

Circular diffraction pattern depends onAperture radius, a

smaller - more diffraction & wider patternwavelength

longer wavelengths diffract more

So two objects separated by ½ that can be resolved as separate bright spots = “Rayleigh Criterion”

acenter 22.1

2

aRayleigh

22.1