The Nature of Light. Light is a propagating electromagnetic waves

Transcription

1 The Nture of Light Light is propgting electromgnetic wves

2 Index of Refrction n: In mterils, light intercts with toms/molecules nd trvels slower thn it cn in vcuum, e.g., vwter The opticl property of trnsprent mterils is clled the Index of Refrction: Since v mteril < c lwys, n >1! n 3 4 c c (Tble 33.1) v mteril

3 Index of Refrction nd Wve Aspects of Light medium b medium b e+ Oscillting e+ Source of EM wve n c v n b c v b The wvelength of light chnges in different medium ccordingly, n n b b With one medium being vcuum, we hve n n

4 The Study of Light: Optics Condition for Rys Optics: L L Relevnt system size >> wvelength glss In this pproximtion, wve chrcteristic of light is not importnt nd rys model of light gives ccurte predictions. (Visible light: ~ 500 nm << L Rys Optics works well with typicl opticl instruments: mirror, lens, cmers, telescopes, ) Physicl (Wve) Optics (Ch.35-36): The study of light when wve properties of light re importnt (diffrction nd interference). L

5 Reflection nd Refrction incident ry norml reflected ry Plne of incidence r ir mteril (n ) boundry/interfce between two medi glss mteril b (n b ) refrcted ry b When light hits boundry, typiclly prt of it will be reflected & prt of it will be refrcted.

6 Lw of Reflection incident ry norml reflected ry r mteril (n ) mteril b (n b ) (ngle of reflection) (ngle of incidence) r

7 Lw of Refrction (Snell s Lw) incident ry norml reflected ry mteril (n ) mteril b (n b ) refrcted ry b n sin n sin b b

8 Totl Internl Reflection Light moves from medium with lrger n to one with smller n. As the ngle of incidence becomes more nd more cute, the light ceses to be trnsmitted, only reflected. At the interfce, sin crit n n b

9 A Linerly Polrized EM Wve For n electromgnetic wve, the direction of the electric field vector gives the polriztion of the wve. E ( x, t) An trnsverse electromgnetic wve with polriztion in the y-direction: E( x, t) Emx cos( kxt)ˆj ( x, t) B ˆ B mx cos( kxt) k A polrized wve in well defined direction is clled linerly polrized wve.

10 Polriztion by Polrizing Filter Since intensity (I) is proportionl to E 2, I I trns cos 2 mx (Mlus s Lw) Trnsmitted intensity of linerly polrized light through polrizer

11 Polriztion by Reflection At the specil ngle (polrizing ngle or Brewster s ngle) p, the electric field component prllel to the plne of incidence will not be reflected! (Brewster s Lw) tn p n b n

12 Summry for Mirrors & Lens The following re vlid for both converging nd diverging lens if we follow the proper sign conventions (object-imge reltion, lens & mirrors) s s' f n 1 f R R 1 2 f R 1 2 (focl length, lens) (focl length, mirrors) m s ' s (lterl mgnifiction, lens & mirrors)

13 Sign Rules for Mirrors & Lens 1. Object Distnce: s is + if the object is on the sme side s the incoming light (for both reflecting nd refrcting surfces) nd s is otherwise. 2. Imge Distnce: s is + if the imge is on the sme side s the outgoing light nd is otherwise. 3. Object/Imge Height: y (y ) is + if the imge (object) is erect or upright. It is if it is inverted. 4. Rdius of Curvture: R is + when the center of curvture C is on the sme side s the outgoing light nd otherwise. 5. Focus Length: (+ concve, - convex) (+ converging, - diverging)

14 Geometric Methods: Rys Trcing Principl rys for concve mirror

15 Geometric Methods: Rys Trcing Principl rys for convex mirror (might need to extrpolte lines to intersect t imge point)

16 Ry Trcing Methods for Lenses Focl Point on the outgoing side

17 Rys Trcing Methods for Lenses Focl Point on the incoming side

18 Wve Nture of Light Previous Chpters (Geometric Optics) << L Rys Model is n pproximtion of EM wves with rys pointing in the direction of propgtion Next Couple of Chpters (Wve/Physicl Optics) ~ L Like wter wves, light spreds nd interferes with ech other. Observed phenomen cnnot be ccounted for by rys: Diffrction Interference spreding constructive/ destructive interference ptterns

19 Single Slit Diffrction

20 Single-Slit Diffrction: Drk Fringes For higher order minimum with lrger ngulr distnce, we cn use the sme rgument by subdividing the slit into more groups (6, 8, 10, etc.). This leds to the following generl formul for the drk fringes: sin m, m1, 2, Note: 1. m = 0 is not the first minimum! In fct, it is the loction for the centrl mx. 2. Secondry mximum occurs ner 3/2, 5/2, etc. but not exctly.

21 Intensity in Single-Slit Pttern Then, lstly wiith,the intensity of the pttern s function of is, 2 sin 2 0 sin sin sin I I Intensity sin

22 Double-Slit Interference Pttern (w/o diffrction) d S 2 S 1

23 Constructive/Destructive Two-Slit Interference Applying the conditions for constructive/ destructive interference, we hve the following conditions: Constructive Interference: Two Slit Interference dsin m ( m0, 1, 2, ) Destructive Interference: Two Slit Interference 1 dsin m ( m0, 1, 2, ) 2 The bright/drk bnds in the pttern re clled fringes m is the order of the fringes

24 Intensity in Two-Slit Interference Putting this expression for the phse difference into our previous intensity eqution for two-slit interference pttern, we hve, I 2 d I0 cos sin

25 Full Double-Slit Diffrction Pttern Combined effects of interference from both slits diffrction from individul slit d

26 Diffrction Ptterns from Multiple Slits loctions of Mxs sty the sme dsin m ( m0, 1, 2, ) N lrger peks get shrper

27 Resolving Power for Circulr Apertures Consider two non-coherent point sources (so tht they don t interfere), i.e. two distnt strs, ngulr seprtion between the two strs str 1 str 2 lens from telescope We will observe two diffrction ptterns on top of ech others.

28 Resolving Power for n Apertures The Limit of Resolution for n perture is defined s the smllest ngulr seprtion between two light sources tht cn be resolved ccording to the Ryleigh s Criterion nd it is given by: Circulr Aperture sin min 1.22 D Single Aperture sin min

29 Interference in Thin Films Color fringes observed from n oil slick on wter or on sop bubble re the white-light interference ptterns produced by the reflected light off thin film of oil or sop.

30 Phse Shifts During Reflection From Mxwell s Equtions, one cn show tht the reflected wve will suffer 180 o or /2 phse shift if it is reflected off from medium with higher n. E r n n n n b b E i (for norml incidence)