Lecturer: Ivan Kassamakov, Docent Assistants: Risto Montonen and Anton Nolvi, Doctoral

Transcription

1 Lecturer: Ivan Kaamakov, Docent Aitant: Rito Montonen and Anton Nolvi, Doctoral tudent Coure webpage: Coure webpage:

2 Peronal inormation Ivan Kaamakov oice: PHYSICUM - PHY C 38 (9:00-9:00) Rito Montonen rito.montonen@helinki.i oice: PHYSICUM - PHY A 3 Anton Nolvi anton.nolvi@helinki.inolvi@helinki oice: PHYSICUM - PHY C 37

3 Schedule: Lecture: Tueday: 0:5 :00, , Lecture Room: PHYSICUM - PHY D6 SH; Exercie: Tueday: :5 4:00, , Lecture Room: PHYSICUM - PHY D6 SH; Demontration: Demontration: Electronic Laboratory: PHYSICUM - PHY C 3-36.

4 Lecture Lecture # Week # Place - Lecture Room Date Starting time Ending time 0 OPTIIKKA : LUENTO 3 PHYSICUM - PHY D6 SH :5 :00 0 OPTIIKKA : LUENTO 4 PHYSICUM - PHY D6 SH :5 :00 03 OPTIIKKA : LUENTO 5 PHYSICUM - PHY D6 SH :5 :00 04 OPTIIKKA : LUENTO 6 PHYSICUM - PHY D6 SH :5 :00 05 OPTIIKKA : LUENTO 7 PHYSICUM - PHY D6 SH :5 :00 06 OPTIIKKA : LUENTO 8 PHYSICUM - PHY D6 SH :5 :00 07 OPTIIKKA : LUENTO 9 PHYSICUM - PHY D6 SH :5 :00 08 OPTIIKKA : LUENTO PHYSICUM - PHY D6 SH :5 :00 09 OPTIIKKA : LUENTO PHYSICUM - PHY D6 SH :5 :00 0 OPTIIKKA : LUENTO 4 PHYSICUM - PHY D6 SH :5 :00 OPTIIKKA : LUENTO 5 PHYSICUM - PHY D6 SH :5 :00 OPTIIKKA : LUENTO 6 PHYSICUM - PHY D6 SH :5 :00 3 OPTIIKKA : LUENTO 7 PHYSICUM - PHY D6 SH :5 :00 4 OPTIIKKA : LUENTO 8 PHYSICUM - PHY D6 SH :5 :00

5 Exercie Exercie # Week # Place - Lecture Room Date Starting time Ending time 0 OPTIIKKA : LUENTO 3 PHYSICUM - PHY D6 SH :5 6:00 0 OPTIIKKA : LUENTO 4 PHYSICUM - PHY D6 SH :5 6:00 03 OPTIIKKA : LUENTO 5 PHYSICUM - PHY D6 SH :5 6:00 04 OPTIIKKA : LUENTO 6 PHYSICUM - PHY D6 SH :5 6:00 05 OPTIIKKA : LUENTO 7 PHYSICUM - PHY D6 SH :5 6:00 06 OPTIIKKA : LUENTO 8 PHYSICUM - PHY D6 SH :5 6:00 07 OPTIIKKA : LUENTO 9 PHYSICUM - PHY D6 SH :5 6:00 08 OPTIIKKA : LUENTO PHYSICUM - PHY D6 SH :5 6:00 09 OPTIIKKA : LUENTO PHYSICUM - PHY D6 SH :5 6:00 0 OPTIIKKA : LUENTO 4 PHYSICUM - PHY D6 SH :5 6:00 OPTIIKKA : LUENTO 5 PHYSICUM - PHY D6 SH :5 6:00 OPTIIKKA : LUENTO 6 PHYSICUM - PHY D6 SH :5 6:00 3 OPTIIKKA : LUENTO 7 PHYSICUM - PHY D6 SH :5 6:00 4 OPTIIKKA : LUENTO 8 PHYSICUM - PHY D6 SH :5 6:00

6 Thin Lene A len conit o a piece o gla or platic, ground o that each o it two reracting urace i a egment o either a phere or a plane Simple len : One element len Compound len : Many element len Thin or thick-that that i, whether or not it thickne i eectively negligible We will only conider thin lene where the thickne o the len i mall compared to the object and image ditance. Thee are example o converging g lene They have poitive ocal length They are thicket in the middle Thee are example o diverging lene They have negative ocal length They are thicket at the edge

7 Thin Len Equation I the len i thin enough, d 0. Aume n m =, we have the thin len equation (len maker ormula): o i ( n l ) R R n m R R lim lim S C C o ( n l i i ) R o R P' o io V V n l d i P Gauian len ormula: o i Paraxial ray approximation:. Ray nearly parallel to the optical axi. All angle and h are mall => co, in 3. Snell law n o θ o = n i θ i 7

8 Thin Len Optical Center Optical center o a len: All ray whoe emerging direction are parallel to their incident direction pa through one common point. C A C R O R B Triangle AOC I and BOC are imilar, in the geometric ene, and thereore their ide are proportional. AC //BC C O/OC = R /R O doe not depend on AB. For a thin len, ray paing through h the optical center are traight ray. The paraxial ray travering AB enter and leave the len in the ame direction Ray paing through 0 may, accordingly, be drawn a traight line.

9 Focal and Image plane A bundle o parallel paraxial ray incident on a pherical reracting urace come to a ocu at a point on the optical axi. C For paraxial ray, σ become a plane near the optical axi Focal plane Focal plane: In paraxial optic, a len ocue any bundle o parallel ray onto a urace that contain the ocal point and i perpendicular to the optical axi. F i Focal plane

10 Finite Imagery Thu ar we've treated the mathematical abtraction o a ingle-point ource. Now let' deal with the act that a great many uch point combine to orm a continuou inite object Real and virtual image: A real image i ormed when light ray converge to and diverge rom the image point. Can be diplayed on a creen. A virtual image i ormed when light ray do not converge to the image point but only appear to diverge rom that point. Cannot be diplayed on a creen. Image are alway located by extending diverging ray back to a point at which they interect. Image plane: In paraxial optic, the image ormed by a len o a mall planar object normal to the optical axi will alo be a mall plane normal to that axi.

11 Thin Convex Len Ray Trace S O F i P S F o 3 P Ray through optical center O Parallel ray rom S mut pa through F i 3 Ray through F o mut emerge parallel

12 Ray Tracing Diagram and Magniication Three key ray in locating an image point: ) Ray through the optical center: a traight line. ) Ray yparallel to the optical axi: emerging paing through the ocal point. 3) Ray paing through the ocal point: emerging parallel to the optical axi. Tranvere magniication: M T yi i y o o Longitudinal magniication: M L dxi dx o x o M T S' y A o F o O F i P S 3 B P' x o x i o Meaning o ign or lene: + - o Real object Virtual object i Real image Virtual image Converging Diverging len y o Erect object Inverted object y i Erect image Inverted image i y i

13 Focuing Light in the Real World Light can not be ocued through an aperture maller than a diraction-limited it d pot pot radiu. D D z d / Depth o ocu z =. x 4(/D) co - mall angle z =. /NA

14 Len example Microcope objective Microcope objective Spot ize =. / ( NA) NA = nd/ = nin Example: NA =.3, pot ize: d / = / D z d /

15 Focuing Light in the Real World min min ource ize In cae we want to collimate: limitation it ti will alway be at leat min increaing may be required to reduce pot ize at the expene o looing light

16 Len equation - Newtonian orm A thin len can be replaced by a plane From the geometry o imilar triangle: AOF i and P P F i From the geometry o imilar triangle: S S O and P P O From () and () Gauian len equation o i From the geometry o imilar triangle: BOF o and S S F o From () and (3) x o x i Newtonian len equation y y o i ( i ) () yo o y () i i y i (3) ( 0 ) y o

17 Convex Len - Virtual Image P S P F o S O F i

18 Convex Len - Virtual Image

19 Concave Len - Virtual Image S P S F o P O F i

20 AF 36-6 Thin Lene

21 Image orming behavior o a thin poitive len len.

22 Thin Len Combination 4 O O F i F i F o F o d<, d< d o i Locating the inal image o L +LL uing ray diagram: ) Contructing the image ormed by L a i there wa no L. ) Uing the image by L a an object, locating the inal image. The ray through O (Ray 4, mut be backward) i needed.

23 Pretend len not there F F

24 Add nd len and trace ray rom t len image F F

25 Two thin lene eparated by a ditance maller than either ocal length. Note that d < i, o that the object or virtual Len (L) i virtual. d<, d< The additional convergence caued by L o that the inal image i cloer to the object. Ray 4 enable the inal image i tto be b llocated t d graphically.

26 Thin Len Combination I the econd len i inide the ocu o the irt: Convex len horten the ocal length Concave len lengthen the ocal length d<, d<

27 Thin Lene in Contact For len in contact (eparation i negligible) Object ditance o len # = Image ditance o len # For an object at ininity: or :

28 Analytical calculation o the image poition P S F o F o F i O O F i S d i i o i i a unction o ( o,,, d) d i o i ( o,,, ) Gauian len equation => The total tranvere magniication (M T ) ) /( ) /( d d i i o i o M M M o i o i T T T ( ) 0 0 d i o i o d o o i

29 Analytical calculation o the image poition Back ocal length (bl): Ditance rom the lat urace to the nd ocal point o the ytem. Let o d d Front ocal length ( l): Ditance rom the irt urace to the t ocal point o the bl d d d d i Front ocal length (..l.): Ditance rom the irt urace to the ocal point o the ytem. Let i then thi give o ; o = d i = i = d but : d l d d l d S i i o i o ) d = + : Both l and bl are ininity. Plane wave in, plane wave out (telecope). ) d 0: l bl = eective ) d 0: 3) N lene in contact: e e l bl e = eective ocal length ). N e

30 Sytem o N thin lene in contact Sytem o N lene whoe thicknee are mall and each len i placed in contact with it neighbor. 3 N Then, in the thin len approximation:... e 3 N Fig 5 3 A poiti e and negati e thin len combination or a Fig. 5.3 A poitive and negative thin len combination or a ytem having a large pacing between the lene. Parallel ray impinging on the irt len enable the poition o the bl.

31 Thin Len Combination Two identical converging (convex) lene have = = +5 cm and eparated by d = 6 cm. o = 0 cm. Find the poition and magniication o the inal image. o i o i M T M i = -30 cm at (O ) which i virtual and erect Then o = i + d = 30 cm + 6 cm = 36 cm i = i = +6 cm at I The image i real and inverted i i TM T o o.7 An object o height y o = cm ha an image height o y i = -.7cm

32 Thin Len Combination = + cm, = -3 cm, d = cm An object i placed 8 cm to the let o the irt len ( o = 8 cm). o i i = +36 cm in back o the econd len, and thu create a virtual object or the econd len. Image i real and Inverted o = - 36 cm cm = -4 cm M T o M i i o i = i = +5 cm; The magniication i given by i TM T o 3.57 I y o = cm thi give y i = cm

33 Limit o the Thin Len Model 3 aumption :. All ray rom a point are ocued onto image point Remember thin len mall angle aumption. All image point in a ingle plane 3. Magniication M T i contant Deviation rom thi ideal are aberration

34 Planar Mirror ) o = i, i = r. ) Sign convention or mirror: o and i are poitive when they lie to the let o the vertex. 3) Image inverion - relection rom a ingle mirror caue a right-handed h d (rh) object to appear a a let-handed (lh) image 4) Sytem with more than one mirror give rie to an odd or even number o relection, reulting in r-h l-h or r-h r-h ymmetry, repectively. 5) The tranvere magniication i imply M T = -S i /S o = +

35 l-h r-h Inverion l-h r-h Inverion

36 l-h r-h Inverion

37 AF 36-0 Image Formed by Spherical Mirror

38 AF 36-8 Image Formed by a Flat Reracting Surace

39 Ellipoidal Relector Ued in Condener 39

40 Apherical mirror ) Conic ection curve: paraboloid, hyperboloid, ellipoid. ) Real and virtual image 3) O-axi optic. Paraboloid A O F F B C Second Focu i at ininity I F F F Perect Image at ininity parallel ray Alo-ocue a parallel beam into a point

41 Paraboloidal Relector olar energy collection, eicient area illumination, high- power ource collimation, and portable narrowbeam potlamp o high brightne and eiciency.

42 O-Axi Paraboloidal Relector Uer ha unretricted acce to the ocu 4

43 Uing pherical ection to approximate parabolic relection: parabolic relection: / y R R R R y R R R x Rx y R R x y 0 R y R R y R R y x x Rx y Conider y/r << and x < R, ue a binomial expanion / / / 4 ) ( 4 R x Rx y y O R y x y R Paraxial region y 4 x Paraxial region y << R Equation or a parabola

44 The Mirror Formula A SC SA CP PA ince i = r SA o PA i S C i r P F i V Paraxial Approx. o R ( i R) o i o i R R R o i, o i o o Mirror Formula

45 Finite imagery Four key ray in inding an image point: ) Ray through the center o curvature. ) Ray parallel to the optical axi. 3) Ray through the ocal point. 4) Ray pointing to the vertex. S C 4 3 P F V I) Concave mirror, the image can be real or virtual. i) p > R/, the image i real, inverted. ii) p = R/, the image i ininitely ar. iii) P < R/, the image i virtual, upright. II) Convex mirror, the image i virtual and upright. Tranvere magniication: M T yi i y o o

46 Ray diagram: concave mirror Erect Virtual Enlarged C ƒ e.g. having mirror

47 Ray diagram: convex mirror Erect Virtual Reduced ƒ C

48 AF 36-3 Image Formed by Spherical Mirror