Geometrical Optics Mirrors and Prisms

Transcription

1 Phy 322 Lecture 4 Chapter 5 Geometrcal Optc Mrror and Prm

2 Optcal bench

3 Mrror Ancent bronze mrror Hubble telecope mrror Lqud mercury mrror

4 Planar mrror alo called plane, or flat mrror r = - o Sgn conventon: on the object de potve, and negatve on the oppote de

5 Planar mrror Sgn conventon: on the object de potve, and negatve on the oppote de = - o For a plane mrror, a pont ource and t mage are at the ame dtance from the mrror on oppote de; both le on the ame normal lne. Image vrtual, up-rght, and lfe-ze (M T = +) The equaton for len work: M T y y o o

6 Exerce: plane mrror heght How hgh hould be the mrror for a peron to ee a full mage of hm/her-elf? Soluton: A B D C Trangle ABC twce a mall a ADE E BC half DE (the heght of the guy). Mrror (BC) hould be at leat half of the guy heght (DE) 2. It bottom hould /2 of the heght of guy eye from the ground

7 Mrror mage Mrror mage of left hand a rght hand Inveron: convertng rght-handed coordnate ytem nto left-handed one Even number of mrror can be ued to avod nveron

8 Applcaton: teerng lght DLP projecton TV reflex camera (SLR) Atomc force mcrocope

9 Parabolc aphercal mrror V Make a mrror that wll converge plane wave nto a pont Fermat prncple: OPL W A A F W2 A2 A2 F Applcaton: headlght, W A A D W2 A2 A2 D2 flahlght, A F A D A2 F A2 D radar, 2 dh antenna, In general: AF AD. Th the urface of parabolod: y 2 = 4fx (orgn at vertext V)

10 Aphercal mrror dvergngdvergng convergngdvergng off-ax parabolc Collect lght from one pont to another convergngconvergng dvergngconvergng

11 Sphercal mrror y 2 4 fx Parabolod and phere are mlar n paraxal approxmaton y y 2 2 x 2 2 x R R y x 2xR 2 2 2xR R R mall when cloe to ax x

12 Sphercal mrror formula SAP bected by AC: SC SA CP PA Paraxal approxmaton: o R o o R 2 R SA o PA Focal length: f lm/ / f 2/ R o o o f lm/ / f 2/ R o SC o R CP Sgn conventon: R R<0 n real object pace o >0 n real object pace >0 n real mage pace f >0 concave mrror Mrror Formula 2 f R o

13 Sphercal mrror o f 2 R Note: Both mrror and len equaton are the ame, except the real mage n front of mrror, but t behnd the len Magnfcaton equaton are the ame a well.

14 Concave mrror: prncpal axe and mage Prncpal ray for concave mrror: ) Parallel to prncpal ax reflect through F. o f 2 R 2) Through F, reflect parallel to prncpal ax. 3) Through center. S # #3 f Image : C Real (lght ray actually cro) Inverted (Arrow pont n oppote drecton) Dmnhed (maller than object, only f object further than C) NOTE: Any other ray from object tp whch ht mrror wll reflect through mage tp #2

15 Convex mrror: prncpal axe and mage Prncpal ray for convex mrror: ) Parallel to prncpal ax appear to orgnate from F after reflecton. 2) Through F, reflect parallel to prncpal ax. 3) Through center. # S #2 #3 P Image : f Vrtual (lght ray don t really cro) Uprght (ame drecton a object) Dmnhed (maller than object) **For a real object, mage alway vrtual, uprght and dmnhed F C

16 Exerce: can a concave mrror form a vrtual mage? o f o Concave mrror: o and f are alway potve, want to get negatve f o 0 vrtual mage o f An object mut be between mrror and t focal plane F o

17 Sphercal mrror

18 Example

19 Dperng prm n n n t n t Bendng depend on wavelength: dperng prm,.e. n=n() Can we ue optcal flat for dperng lght? Ray emerge parallel to each other. Practcally we don t ee them (focued by the eye at the ame pot).

20 Dperng prm equaton n n n t n t t2 Example n = n t =n Total devaton a functon of refracton ndex: 2 2 arcn n n n t n co Mnmum devaton mn occur when = t2 n n mn / 2 n / 2 can ue to determne n

21 Spectral analyzer And th arrangement map poton to angle: out xn

22 Prm pectrometer Drawback: () - nonlnear dependence Low pectral reoluton Small aperture

23 Contant-devaton dperng prm Pelln-Broca prm: Abbe prm: mn =90 o alway! Pelln, Ph. and Broca, André (899), "A Spectrocope of Fxed Devaton". Atrophycal Journal Ernt Abbe mn =60 o alway! Fx nput-output at 90 o or 60 o and rotate prm for dfferent wavelength

24 Reflectng prm Reflect the beam wth no dperon ung total nternal reflecton If we make t = 2 - lke n flat gla plate = 2 + achromatc prm

25 Reflectng prm The rght-angle prm The Porro prm The penta prm The Dove prm