27 Refraction, Dispersion, Internal Reflection

Transcription

1 Chapter 7 Refractio, Dispersio, Iteral Reflectio 7 Refractio, Dispersio, Iteral Reflectio Whe we talked about thi film iterferece, we said that whe light ecouters a smooth iterface betwee two trasparet media, some of the light gets through, ad some bouces off. re we limited the discussio to the case of ormal icidece. (Recall that ormal meas perpedicular to ad ormal icidece is the case where the directio i which the light is travelig is perpedicular to the iterface.) Now we cosider the case i which light shiig o the smooth iterface betwee two trasparet media, is ot ormally icidet upo the iterface. Here s a clea depictio of what I m talkig about: R ad here s oe that s all cluttered up with labels providig termiology that you eed to kow: Normal Trasmitted Ray, a.k.a. the Refracted Ray Agle of Refractio straightahead path. idex of refractio of the medium i which the light is travelig after it passes through the iterface. iterface betwee the two trasparet media. R idex of refractio of the medium i which the light is origially travelig. Icidet Ray Agle of Icidece Normal Agle of Reflectio 37 Reflected Ray at R = i Accord with the Law of Reflectio

2 Chapter 7 Refractio, Dispersio, Iteral Reflectio As i the case of ormal icidece, some of the light is reflected ad some of it is trasmitted through the iterface. Here we focus our attetio o the light that gets through. Experimetally we fid that the light that gets through travels alog a differet straight lie path tha the oe alog which the icomig ray travels. As such, the trasmitted ray makes a agle with the ormal that is differet from the agle that the icidet ray makes with the ormal. adoptio of a ew path by the trasmitted ray, at the iterface betwee two trasparet media is referred to as refractio. trasmitted ray is typically referred to as the refracted ray, ad the agle that the refracted ray makes with the ormal is called the agle of refractio. Experimetally, we fid that the agle of refractio is related to the agle of icidece by Sell s Law: where: = (7-) si si is the idex of refractio of the first medium, the medium i which the light is travelig before it gets to the iterface, is the agle that the icidet ray (the ray i the first medium) makes with the ormal, is the idex of refractio of the secod medium, the medium i which the light is travelig after it goes through the iterface, ad, is the agle that the refracted ray (the ray i the secod medium) makes with the ormal. 38

3 Chapter 7 Refractio, Dispersio, Iteral Reflectio Dispersio O each side of the equatio form of Sell s law we have a idex of refractio. idex of refractio has the same meaig as it did whe we talked about it i the cotext of thi film iterferece. It applies to a give medium. It is the ratio of the speed of light i that medium to the speed of light i vacuum. At that time, I metioed that differet materials have differet idices of refractio, ad i fact, provided you with the followig table: Medium Idex of Refractio Vacuum Air.00 Water.33 Glass (Depeds o the kid of glass. Here is oe typical value.).5 What I did t metio back the is that there is a slight depedece of the idex of refractio o the wavelegth of the visible light, such that, the shorter the wavelegth of the light, the greater the idex of refractio. For istace, a particular kid of glass might have a idex of refractio of.49 for light of wavelegth 695 m (red light), but a idex of refractio that is greater tha that for shorter wavelegths, icludig a idex of refractio of.5 for light of wavelegth 405 m (blue light). effect i the case of a ray of white light travelig i air ad ecouterig a iterface betwee air ad glass is to cause the differet wavelegths of the light makig up the white light to refract at differet agles. blue gree red Glass Icomig White Light Air This pheomea of white light beig separated ito its costituet wavelegths because of the depedece of the idex of refractio o wavelegth, is called dispersio. 39

4 Chapter 7 Refractio, Dispersio, Iteral Reflectio Total Iteral Reflectio I the case where the idex of refractio of the first medium is greater tha the idex of refractio of the secod medium, the agle of refractio is greater tha the agle of icidece. > For such a case, look what happes whe we icrease the agle of icidece, : > agle of refractio gets bigger 40

5 Chapter 7 Refractio, Dispersio, Iteral Reflectio util evetually it (the agle of refractio) gets to be 90. > It ca t get ay bigger tha that, because, beyod that, the light is ot goig through the iterface. A agle of refractio greater tha 90 has o meaig. But, ote that we still have room to icrease the agle of icidece. What happes if we cotiue to icrease the agle of icidece? Well, ideed, o light gets through the iterface. But, remember at the begiig of this chapter where we talked about how, whe light is icidet o the iterface betwee two trasparet media, some of the light gets through ad some of it is reflected? Well, I have t bee icludig the reflected ray o our diagrams because we have bee focusig our attetio o the trasmitted ray, but, it is always there. thig is, at agles of icidece bigger the the agle that makes the agle of refractio 90, the reflected ray is all there is. pheomeo, i which there is o trasmitted light at all, just reflected light, is kow as total iteral reflectio. agle of icidece that makes the agle of refractio 90 is kow as the critical agle. At ay agle of icidece greater tha the critical agle, the light experieces total iteral reflectio. Note that the pheomeo of total iteral reflectio oly occurs whe the light is iitially i the medium with the bigger idex of refractio. Let s ivestigate this pheomeo mathematically. Startig with Sell s Law: si si = solved for the sie of the agle of refractio: si = si we ote that, sice it was stipulated that >, the ratio / is greater tha. si is always less tha, but, if is big eough, si ca be so close to that the right-had side of 4

6 Chapter 7 Refractio, Dispersio, Iteral Reflectio the equatio si = si is greater tha. I that case, there is o that will solve the equatio because there is o agle whose sie is greater tha. This is cosistet with the experimetal fact that, at agles of icidece greater tha the critical agle, o light gets through the iterface. Let s solve for the critical agle. At the critical agle, the agle of refractio is 90. Let s plug that ito the equatio we have bee workig with ad solve for : evaluated at = 90 yields: si si 90 = si o = si = si si = = si This is such a special agle of icidece that we ot oly give it a ame (as metioed, it is called the critical agle), but, we give it its ow symbol. critical agle, that agle of icidece beyod which there is o trasmitted light, is desigated C, ad, as we just foud, ca be expressed as: si = (7-) C 4