Physics 116 Lecture 20 Optical Instruments Nov 1, 2011 R. J. Wilkes - PowerPoint PPT Presentation

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 – � Objective lens forms real image of object inside telescope tube – � Eye lens is used as magnifier to view real image made by objective Refractor • � 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 Newtonian • � Easier to make in large sizes Reflector 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 F’ O y F E • � Galilean / non-inverting / “opera glass” • � Objective is positive and eyepiece is negative • � Image is erect and viewed at infinity F’ O y F E • � In both cases, the objective makes a real image at the eyepiece focal point 6

Telescopes refractor reflector Gran Telescopio Canarias, 410” Galilean reflector, Canary Islands (2009) Yerkes refractor, 40”, Wisconsin (1897) Photos: Edmunds Scientific, REI, Wikipedia 7

Angular vs linear magnification • � Linear magnification is • � Angular magnification is • � Telescopic systems, designed for viewing objects at d o = 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!)

!"#$%"&'$($ !"#$%&#%'( $#")*+$ ,&)-$'./.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$165&$ Real, inverted image from Your eye is objective lens part of the F E optical system ! F O object Objective lens, Eye lens, focal length F E focal length F o (magnifier) retina Virtual image formed by eye lens cornea/lens – � >-&$0&7'$(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&$$ 9

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 10

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$(K.'$ Lens plane object 1 2 f ’ +x o o o f 3 image l ’ l

U6//()-$"9$0&7'$5&?(=.");$3"'.<=&V9$0&7'&'$ d o greater than f object 1 Example: camera, or projector 3 f f o o o 2 Focal pt Focal pt image Object distance Image distance d O d I Rays from object tip re-converge at a point, forming a real, inverted, magnified image ( d I is positive) object 2 d o less than f 1 Example: Magnifying glass image f Focal pt f o o o Focal pt Object distance d O Rays appear to emerge from a virtual, erect, magnified image, lens equation gives negative d I Image distance d I

U6//()-$"9$0&7'$5&?(=.");$7&8(<=&V9$0&7'&'$ image d o greater than f object 1 Example: eyeglasses for myopia 2 o o o Focal pt f Gazing through the lens toward Object distance the object, we see rays d O appearing to emerge from a virtual, erect, demagnified image Image distance that is closer than the object, d I lens equation gives negative d I d o less than f Very little difference – image just moves a bit closer to the lens QT$

Not On Test! 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 F R F B F Y F R - F B = ACA (Axial Chromatic • � Index of refraction n=n( ! ) Aberration) – � For most materials, n decreases with increasing ! • � so n BLUE > n YELLOW > n RED • � we get different focal points for different colors: BK1 Typical optical glass n vs l curve: CA is positive for converging lenses, F2 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 marginal ray " M paraxial ray " P PF MF • � The difference is called spherical aberration: • � Any refracting surface with spherical shape will have SA Narrowest point • � Envelope of ray paths is the Caustic Surface MF – � Neck of caustic = Circle of Least Confusion position at which image of a distant x pinhole is smallest PF caustic surface

W'<8/(<2$(5&))(<"7$ Not On Test! X?(1O'$('<8/(<'/$+$$ • � – � W'<8/(<'/$.'$(7$(5&))(<"7$#?&)&$0.8?1$)(-'$'1).*.78$1?&$0&7'$(1$3".71'$(#(-$9)"/$1?&$ (K.'$?(=&$%.Y&)&71$9"2(0$3".71'4$%&3&7%.78$63"7$1?&$3"'.<"7$"9$1?&$()).=(0$3".71Z$ • � [")$&K(/30&4$=&)<2(0$(7%$?").N"71(0$'3"*&'$"9$($#?&&0$8&1$9"26'&%$(1$%.Y&)&71$ %.'1(72&'Z$ – � @))&860()$26)=(16)&$"9$2")7&($/(*&'$1?&$&-&$0&7'$('<8/(<2$ – � C"))&2<=&$0&7'&'$9")$('<8/(<'/$?(=&$($2-0.7%).2(0$G.7'1&(%$"9$'3?&).2(0I$3)"A0&$$ If only vertical, or only horizontal spokes appear sharp, you may have astigmatism 17