Physics 116
Lecture 20
Optical Instruments
Nov 1, 2011
R. J. Wilkes
Email: ph116@u.washington.edu
Lecture Schedule
(up to exam 2)
Today
2
Announcements
•!
Physics Study Center now staffed by TAs an hour later on
M-W: 9:30 am to 6:30 pm M-W, 9:30am-5:30pm Th,
10:30am-5:30pm F.
•! Exam 2 next Monday: same procedures as last time
•! Practice exam posted Thursday, in class Friday
•! YOU bring bubble sheet, pencil, calculator
Optical instruments
•! We can put together systems of lenses, mirrors, prisms,
polarizers, filters, beam splitters, and all the other optical
components we have discussed, to make a variety of common
optical instruments, using ray-tracing methods:
–! Magnifiers
–! Microsopes
–! Refracting telescopes
–! Reflecting telescopes
–! Cameras
–! Projectors
4
Telescopes
•! Telescopes do 2 things:
–! collect a lot of light across a big aperture
(opening) and cram this light into your eye
•! Lets you see faint objects
–! magnify angles by ratio of the focal lengths
of the main lens/mirror and eyepiece:
Magnification=F/f
•! So object looks bigger to you
•! Simple operation
Refractor
Newtonian
Reflector
–! Objective lens forms real image of object
inside telescope tube
–! Eye lens is used as magnifier to view real
image made by objective
•! Come in two basic varieties:
–! refractors, dating back to Galileo’s time
(objective = lens)
•! Galilean telescope: negative eyelens
–! Reflectors (mirror), invented by Newton!
–! all big telescopes now are reflectors
•! Only one surface to grind and polish
•! Easier to make in large sizes
5
Telescopes
•! Refracting telescopes come in 2 basic varieties
•! Inverting (astronomical)
•! Objective and eyepiece are both positive lenses
•! Image is inverted and viewed at infinity
•! That means: parallel rays come out as parallel rays, the
magnification is angular, not linear
y
F’O
FE
•! Galilean / non-inverting / “opera glass”
•! Objective is positive and eyepiece is negative
•! Image is erect and viewed at infinity
y
F’O
FE
•! In both cases, the objective makes a real image at the eyepiece focal point
6
refractor
Telescopes
reflector
Galilean
Gran Telescopio Canarias, 410”
reflector, Canary Islands (2009)
Photos: Edmunds Scientific, REI, Wikipedia
Yerkes refractor, 40”,
Wisconsin (1897)
7
Angular vs linear magnification
•! Linear magnification is
•! Angular magnification is
•! Telescopic systems, designed for viewing objects at do = infinity, take
parallel rays in and send parallel rays out – what counts is the angular
magnification since no real image is formed.
object
!
!'
image
Angular size of Sun = ! degree of arc = angular size of Moon
(this coincidence makes total solar eclipses possible!)
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Real, inverted
image from
objective lens
FE
object
Your eye is
part of the
optical
system !
FO
Objective lens,
focal length Fo
Eye lens, focal length FE
(magnifier)
retina
Virtual image formed
by eye lens
cornea/lens
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9
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–!
–!
–!
–!
object
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image
10
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2(/&)($2?.3$
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Lens plane
object
1
2
o
f
l
o
o
f’
+x
3
l’
image
U6//()-$"9$0&7'$5&?(=.");$3"'.<=&V9$0&7'&'$
object
do greater than f
Example: camera, or projector
1
3
f
o
o
f
2
Focal pt
o
Focal pt
Object distance
dO
Image distance
dI
image
Rays from object tip re-converge at a point, forming a real, inverted, magnified image
(dI is positive)
object
do less than f
Example: Magnifying glass
2
image
1
Focal pt
o
f
Object distance dO
Image distance dI
o
f
o
Focal pt
Rays appear to emerge from a virtual, erect,
magnified image, lens equation gives negative dI
U6//()-$"9$0&7'$5&?(=.");$7&8(<=&V9$0&7'&'$
image
object
do greater than f
Example: eyeglasses for myopia
1
2
o
Focal pt
o
o
f
Object distance
dO
Image distance
dI
Gazing through the lens toward
the object, we see rays
appearing to emerge from a
virtual, erect, demagnified image
that is closer than the object,
lens equation gives negative dI
do less than f
Very little difference – image just moves a bit closer to the lens
QT$
Lens aberrations
Not On Test!
•! Perfection is impossible!
•! Any real lens will not focus all rays reaching its surface onto the
same focal point
•! Lens Aberrations:
–! Color – different focal points for different wavelengths
–! Spherical aberration – rays arriving at different distances from
the lens axis have different focal points
–! Coma, astigmatism, curvature of field … many more
–! quantitative material on aberrations is “cultural” - not on test!
•! You should understand qualitative descriptions of aberrations
Not On Test!
Chromatic aberration (CA)
•!
•!
Simple lenses make images with ‘rainbows’ around objects in white light
Focal length of lens is different for red, yellow, and blue
FR
FB
•!
FY
Index of refraction n=n(!)
–! For most materials, n decreases with increasing !
•! so nBLUE > nYELLOW > nRED
•! we get different focal points for different colors:
Typical optical glass n vs l curve:
CA is positive for converging lenses,
and negative for diverging.
We can make a doublet with CA=0 by
gluing a negative and positive lens of
different n together
FR - FB = ACA
(Axial Chromatic
Aberration)
BK1
F2
Not On Test!
Spherical aberration (SA)
•!
•!
“Paraxial” ray = ray arriving at lens very close to its optic axis
–! Paraxial ray crosses axis at paraxial focus PF (the ordinary “focal point”)
Marginal ray = ray arriving at lens far from its optic axis
–! Marginal rays parallel to axis cross the axis at marginal focus MF
"M
marginal ray
paraxial ray
"P
PF
MF
•!
•!
•!
The difference is called spherical aberration:
Any refracting surface with spherical shape will have SA
Envelope of ray paths is the Caustic Surface
–! Neck of caustic = Circle of Least Confusion
position at which image of a distant
pinhole is smallest
Narrowest point
MF
x
caustic
surface
PF
Not On Test!
W'<8/(<2$(5&))(<"7$
•!
X?(1O'$('<8/(<'/$+$$
–!
–!
–!
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%.'1(72&'Z$
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If only vertical, or only horizontal
spokes appear sharp, you may
have astigmatism
17