REFLECTION AND REFRACTION

Transcription

1 RFLCTON AND RFRACTON We ext ivestigate what happes whe a light ray movig i oe medium ecouters aother medium, i.e. the pheomea of reflectio ad refractio. We cosider a plae M wave strikig a plae iterface with its directio of propagatio makig a agle θ with the ormal to the surface. We defie the plae of icidece to be the plae determied by k ad ˆ, where ˆ is the ormal to the surface. We split the field ito compoets parallel ad perpedicular to the plae of icidece, ad treat the two cases separately. We choose as show: CAS PARALLL TO PLAN OF NCDNC The sice: ˆk B

2 we will have B directed out of the page as show. Sice we have plae waves we ca write: ik rt 0 ik rt 0 ik 3r3t 3 30 e e e f there are ay boudary coditios at all, they will have to apply at all times ad at all places o the surface. This is oly possible if the expoets are the same at all times ad at all poits o the surface. Thus: where φ t is the agle betwee k i ad r. 3 krcos krcos krcos 3 3 From the drawig we see that: Hece Now we kow that: ksi k si k3 si 3 vk k v /

3 Defie c v where is the idex of refractio. The: ad / 0 0 si si si 3 (agle of icidece = agle of refractio) si si (Sell s Law) 3 These results depeded oly o light beig a wave which is why they were kow log before Maxwell. However to get the relative itesities we do eed the actual form of the boudary coditios. We have already foud them to be: () B cotiuous () ta cotiuous (3) Hta H ta K (4) D D where K is the surface curret/legth ad σ is the surface charge desity. () ad (4) came from: D B0 ad we have already derived them. () ca be foud as follows:

4 Sice the area of the box 0, we get (3) is foud the same way B d ds ds t s s 0 ta ta ta ta H H K H H K ta ta ta ta our case σ = K = 0 ad the boudary coditios are: ta cot Hta cot D cot B cot Hece we have four coditios: Now cos cos 3cos 3 Dsi Dsi D3si B B B3 D D D3 3

5 Thu s we get the three equatios: cos cos () () 3 3 si si 3 H H H3 c c c (3) Now Usig Sell s law this becomes: () si 3si 3 si si v 3 3 v si 3si 3 c c 3 But this is the same as (3). Hece we have two equatios: cos cos cos cos3

6 cos3 cos cos cos 3 cos 3 cos cos3cos But f =, μ = μ these become / / cos3 si 3 si / si cos / si cos 3 3 / / si cos si cos 0 3 as expected.

7 We ca ow calculate the relative itesities as follows: B B ˆ S H k kˆ v The itesity strikig or leavig the plae is: S ˆ Scos Hece N cos c reflected cos c 3 refracted cos3 c reflected N N cos c si refracted 3 cos 3 N cos si / / cos ( ) 4a cos a a( ) cos si / a cos / / With a si

8 Note that / / reflected refracted a cos a cos 4a cos / a a cos cos as expected. Note that whe: O O / a si cos there is o reflected ray with i the plae of icidece. Sice there is oe whe is perpedicular to the plae of icidece (you should check this), we see that reflectio ca produce liearly polarized light. This is the basis for the reductio i glare produced by polarized suglasses as discussed i class. The agle at which this occurs is give by: most cases μ = μ. The a si cos si si si si 4 4

9 ta This is kow as Brewster s agle.