Transcript diffraction and interference

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