Chapter 31: Images and Optical Instruments

Transcription

1 Capter 3: Image and Optical Intrument Relection at a plane urace Image ormation Te relected ray entering eye look a toug tey ad come rom image P. P virtual image P Ligt ray radiate rom a point object at P in all direction.

2 Relection and reraction at a plane urace Image ormation

3 Relection and reraction at a plane urace Image ormation i (or ) i te image ditance i te object ditance: i Sign Rule: () Sign rule or te object ditance: Wen object i on te ame ide o te relecting or reracting urace a te incoming ligt, te object ditance i poitive. Oterwie it i negative. () Sign rule or te image ditance: Wen image i on te ame ide o te relecting or reracting urace a te outgoing ligt, te image ditance i ( or ) i poitive. Oterwie it i negative. (3) Sign rule or te radiu o curvature o a perical urace: Wen te center o curvature C i on te ame ide a te outgoing ligt, te radiu o te curvature i poitive. Oterwie it i negative.

4 Relection at a plane urace Image ormation image i erect image i virtual Multiple image due to multiple Relection by two mirror m / lateral magniication

5 Relection at a plane urace Image ormation Wen a lat mirror i rotated, ow muc i te image rotated?

6 Relection at a perical mirror Concave and convex mirror

7 Relection at a perical mirror Focal point at concave and convex mirror Focal point or ocu: Point F at wic ray rom a ource point are brougt togeter (ocued) to orm an image. Focal lengt: Ditance rom mirror were ocu occur. R/ were R i te radiu o a perical mirror.

8 Relection at a perical mirror Focal point at a concave mirror α γ δ α β γ + + γ δ β + ) /( tan ) /( tan ) /( tan d R d d γ δ β d R d i /, / / << γ δ β R + object image I /, R

9 Relection at a perical mirror Image o an extended object at a concave mirror real image Principle ray: Ligt ray tat can be traced (more eaily) rom te ource to te image:. Parallel to optical axi. Paing troug te ocal point 3. Paing troug te center o curvature 4. Paing troug te center o te mirror urace or len

10 Relection at a perical mirror Magniication o image at a concave mirror m Wen, >0, m<0 inverted / <0, m>0 uprigt or erect

11 Relection at a perical mirror Example wit a concave mirror real image real image real image virtual image

12 Relection at a perical mirror Example wit a concave mirror

13 Relection at a perical mirror Image at a convex mirror + R R m poitive negative (virtual image) R negative negative

14 Relection at a perical mirror Magniication o image at a convex mirror eigt at eigt at m For a convex mirror < 0 eigt at eigt at, + m m > magniied m < minimized m > 0 image uprigt m < 0 image inverted

15 Reraction at a perical urace Reraction at a convex perical urace For mall angle BF( ) AB AB R R /( ) Rn n n φ in AB /( ) /( n n ) n ( ) R n n

16 Reraction at a perical urace Reraction at a concave perical urace For a concave urace, we can ue te ame ormula n ( ) R n n But in ti cae R < 0 and < 0. Tereore te image i virtual.

17 Reraction at a perical urace Relation between ource and image ditance at a convex perical urace R n n n n AB R AB n AB R AB n AB R AB n n ) ( ) ( ) ( ) ( α γ β α β γ β α β γ β Snell law For a convex (concave) urace, R >(<) 0.

18 Reraction at a perical urace Example o a convex urace

19 Reraction at a perical urace Example o a concave urace

20 Reraction at a perical urace Example o a concave urace

21 Reraction at a perical urace Example o a concave urace

22 Convex Len Sign rule or convex and concave len: Sign Rule: () Sign rule or te object ditance: Wen object i on te ame ide o te relecting or reracting urace a te incoming ligt, te object ditance i poitive. Oterwie it i negative. () Sign rule or te image ditance: Wen image i on te ame ide o te relecting or reracting urace a te outgoing ligt, te image ditance i (or ) i poitive (real image). Oterwie it i negative (virtual image). (3) Sign rule or te radiu o curvature o a perical urace: Wen te center o curvature C i on te ame ide a te outgoing ligt, te radiu o te curvature i poitive. Oterwie it i negative.

23 Convex Len Len-maker (tin len) ormula urace urace Image due to urace : n nr n R n n + become ource or urace : R n R n n + + ) ( R n n nr n n + + R >0 R <0 and : R R n ) )( ( + Parallel ray (in.) w.r.t. te axi converge at te ocal point

24 Magniication Convex Len m II / SS SS P II P m m ame a or mirror

25 Convex Len Object between te ocal point and len A virtual image

26 Convex Len Object poition, image poition, and magniication real inverted image m < real inverted image m > virtual erect image m >

27 Type o len Len

28 Two len ytem Len

29 Len Two len ytem (cont d)

30 Len Two len ytem (cont d)

31 Len Two len ytem (cont d)

32 Eye Anatomy o eye

33 Eye Near- and ar-igtedne and corrective lene arigtedne nearigtedne

34 Angular ize d d m i In general te minimum ditance dd min ~5 cm at wic an eye can ee image o an object comortably and clearly.

35 Magniying gla i i virtual image tan M i wen but m i m / / d ( ) i i min d min, d min m 5 cm te eye i mot relaxed te minimum ditance at wic an eye can ee image o an object comortably and clearly. or uman eye.

36 Microcope ) ) /( ( ] / )]/[ ) /( [( / magniier) or a / / ( ) ) /( ( / ) / / / ( / min min Ld d L m M i L L L i m L m object i i i i Q Q,, i L >> mall Object i placed near F ( ~ ). Image by len i cloe to te ocal point o len at F. magniier image ang. ize i

37 Reracting telecope 0 0 / / / / / ) ( / m m i object i i Q angular ize o image by len; eye i cloe to eyepiece image eigt by len at it ocal point Image by len i at it ocal point wic i te ocal point o len image ditance ater len magniier

38 Relecting telecope m / i object /

39 Aberration pere paraboloid

40 Cromatic aberration

41 Gravitational len

42 Problem Exercie Wat i te ize o te mallet vertical plane mirror in wic a woman o eigt can ee er ull-lengt? Solution Te minimum lengt o mirror or a woman to ee er ull eigt I / a own in te igure rigt. -x x x/ (-x)/

43 r 0 Exercie Problem (ocal lengt o a zoom len) ray bundle Q r 0 x d r 0 - I d (variable)< > -d (a) Sow tat te radiu o te ray bundle decreae to x r 0 r0 r0 r0 x r0 r0 d / ) r0 ( d ) / ( r 0 r0 d) / (

44 Exercie Problem (ocal lengt o a zoom len) - I r 0 Q r 0 d (variable)< ray bundle d x r 0 (b) Sow tat te inal image I i ormed a ditance to te rigt o te diverging len. ) ) /( ( d d + d d d d d d d d ) ( ) ( ) (

45 r 0 Exercie Problem (ocal lengt o a zoom len) ray bundle Q r 0 x d r 0 - I d (variable)< (c) I te ray tat emerge rom te diverging len and reac te inal image point are extended backward to te let o te diverging len, tey will eventually expand to te original radiu r 0 at ome point Q. Te ditance rom te inal image I to te point Q i te eective ocal lengt o te len combination. Find te eective ocal lengt. r r r ( d ) r d + d 0 + d