physics 116 optical instruments
TRANSCRIPT
2
Today
Lecture Schedule (up to exam 2)
•! 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
Announcements
4
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
5
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 –! 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 Newtonian
Reflector
Refractor
•! 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
•! Galilean / non-inverting / “opera glass”
•! Objective is positive and eyepiece is negative
•! Image is erect and viewed at infinity
•! In both cases, the objective makes a real image at the eyepiece focal point
6
F’O
FE
y
F’O
FE
y
Telescopes
7
Telescopes
Gran Telescopio Canarias, 410”
reflector, Canary Islands (2009)
Yerkes refractor, 40”,
Wisconsin (1897)
refractor
reflector
Galilean
Photos: Edmunds Scientific, REI, Wikipedia
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.
image
object
! '!
Angular size of Sun = ! degree of arc = angular size of Moon
(this coincidence makes total solar eclipses possible!)
9
!"#$%"&'$($!"#$%&#%'($#")*+$
•! ,&)-$'./.0()$1"$1&0&'2"3&4$561$7"#$#&$#(71$1"$/(*&$(7$./(8&$"9$($
)(*$+,$"5:&21;$(8(.74$"5:&2<=&$0&7'$9")/'$($$(*-$./(8&$.7'.%&$
.7'1)6/&71$165&$
–! >-&$0&7'$(21'$0.*&$($&"!'-(.!*/)"0($$1"$8.=&$=.&#&)$(7$&70()8&%$1"$23*-$
./(8&$"9$1?&$$(*-$./(8&$3)"%62&%$5-$1?&$"5:&2<=&$0&7'$
•! @9$-"6$#(71$1"$3?"1"8)(3?$1?&$"5:&214$361$A0/$")$=.%&"$2?.3$(1$1?&$
)&(0$./(8&$0"2(<"74$")$6'&$2(/&)($0&7'$(B&)$&-&3.&2&$$
FO object
FE
Real, inverted
image from
objective lens
Objective lens,
focal length Fo
Eye lens, focal length FE
(magnifier)
Virtual image formed
by eye lens
Your eye is
part of the
optical system !
cornea/lens
retina
10
C(/&)('$(7%$3)":&21")'$•! C(/&)('$(7%$3)":&21")'$#")*$1?&$'(/&$#(-;$1)(7'9&)$(7$./(8&$9)"/$"7&$
30(2&$1"$(7"1?&)$
–! D)":&21")$#")*'$.7$)&=&)'&;$1)(7'0(1&'$EA0/F$30(7&$1"$'2)&&7$$
–! D.7?"0&$#")*'$('$#&00$('$($0&7'$G561$=&)-$0.H0&$0.8?1$8&1'$1?)"68?I$
–! J6'1$30(2&$"5:&21$9()$9)"/$0&7'$G9()1?&)$1?(7$9"2(0$0&781?$9I$
–! C"/30&K$'-'1&/'$7&&%&%$1"$8.=&$(226)(1&4$'?()3$./(8&$"=&)$9600$./(8&$()&($
object image
D)":&21")$")$2(/&)($
•! L('.2(00-$:6'1$($3"'.<=&$0&7'$9")/.78$($)&(0$./(8&$"7$1?&$'2)&&7$")$
2(/&)($2?.3$
•! C"/30&K$0&7'$'-'1&/'$(00"#$MN""/.78O$G=()-$9"2(0$0&781?$#?.0&$*&&3.78$
./(8&$30(7&$AK&%I4$(7%$&7'6)&$($'?()3$(7%$9(.1?960$./(8&$"=&)$1?&$#?"0&$
(2<=&$()&($"9$1?&$'2)&&7$")$2?.3$
–! P(-$Q$.'$3()(00&0$1"$(K.'$R$3(''&'$1?)"68?$5(2*$9"2(0$3".71$9$O$
–! P(-$S$8"&'$1?)"68?$2&71&)$"9$0&7'$(7%$.'$67%&=.(1&%$
–! P(-$T$8"&'$1?)"68?$9)"71$9"2(0$3".71$9$(7%$&/&)8&'$3()(00&0$1"$1?&$"3<2$(K.'$
o o +x
image
object
Lens plane
f ’ 2
3
1
o
l l ’
f
U6//()-$"9$0&7'$5&?(=.");$3"'.<=&V9$0&7'&'$
image
object
f 3
2
1
Object distance
dO
Image distance
dI
Focal pt
do greater than f
Example: camera, or projector
o o
Focal pt
Rays from object tip re-converge at a point, forming a real, inverted, magnified image
(dI is positive)
f o
image
object
f
2 1
o
Object distance dO
Image distance dI
Focal pt
do less than f
Example: Magnifying glass
o o
Focal pt
Rays appear to emerge from a virtual, erect,
magnified image, lens equation gives negative dI
f
U6//()-$"9$0&7'$5&?(=.");$7&8(<=&V9$0&7'&'$
QT$
image
object
f
2 1
Object distance
dO
Image distance
dI
Focal pt
do greater than f
Example: eyeglasses for myopia
o o o
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
Lens aberrations
•! 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
•! Index of refraction n=n(!)
–! For most materials, n decreases with increasing !
•! so nBLUE > nYELLOW > nRED
•! we get different focal points for different colors:
FB FY
FR
FR - FB = ACA
(Axial Chromatic
Aberration)
BK1
F2
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
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
•! The difference is called spherical aberration:
•! Any refracting surface with spherical shape will have SA
marginal ray
paraxial ray
MF
PF
"M
"P
•! 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
caustic surface
PF
MF
x
Narrowest point
Not On Test!
17
W'<8/(<2$(5&))(<"7$
•! X?(1O'$('<8/(<'/$+$$
–! W'<8/(<'/$.'$(7$(5&))(<"7$#?&)&$0.8?1$)(-'$'1).*.78$1?&$0&7'$(1$3".71'$(#(-$9)"/$1?&$
(K.'$?(=&$%.Y&)&71$9"2(0$3".71'4$%&3&7%.78$63"7$1?&$3"'.<"7$"9$1?&$()).=(0$3".71Z$
•! [")$&K(/30&4$=&)<2(0$(7%$?").N"71(0$'3"*&'$"9$($#?&&0$8&1$9"26'&%$(1$%.Y&)&71$
%.'1(72&'Z$
–! @))&860()$26)=(16)&$"9$2")7&($/(*&'$1?&$&-&$0&7'$('<8/(<2$
–! C"))&2<=&$0&7'&'$9")$('<8/(<'/$?(=&$($2-0.7%).2(0$G.7'1&(%$"9$'3?&).2(0I$3)"A0&$$
Not On Test!
If only vertical, or only horizontal
spokes appear sharp, you may have astigmatism