Physics 3 (PHYF144) Chap 8: The Nature of Light and the Laws of Geometric Optics - 1

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1 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 8. The ature of light Before 0 th etury, there were two theories light was osidered to be a stream of partiles emitted by a light soure. light is a wave Early of 0 th etury: wave-partile duality Wave ature of light The wave theory did ot reeive immediate aeptae for several reasos:. At the time, all the waves kow (soud, water, et) eeded a medium to travel. However, light ould travel to us from the Su through the vauum of spae. [Today s kowledge is ot ultimately orret i future]. If the light were some form of wave it would bed aroud obstales as i soud wave. Soud waves 3. At later time, experimet showed that the light ideed bet aroud the edges of objets. This pheomeo, kow as diffratio, was ot easy to be observed beause light waves have very short wavelegths. Although experimetal evidee ofirmed the wave ature of light, most sietists rejeted the wave theory partly beause of great reputatio of partile theory. Additioal developmets led to the geeral aeptae of the wave theory of light:. Youg's double-slit experimet demostrated that light s iterfere with eah other.. Maxwell s theory of eletromageti wave asserted that light was a form of high frequey EM wave. 3. Hertz ad other ivestigators provided experimetal ofirmatio of Maxwell s theory, ad showed that these waves exhibited refletio, refratio, ad all the other harateristi properties of waves. Wave-partile duality The wave piture of light is ot the whole story, however. Some subsequet experimets ould ot be explaied by it. The most strikig of these is photoeletri effet: Whe light with high frequey eough, regardless of its itesity, strikes o ertai metal surfae, eletros are ejeted from the surfae. I 905, Eistei proposed a explaatio to the photoeletri effet based o the oept of quatizatio developed by Max Plak i 900. The eergy of a eletromageti wave is quatized; it is emitted ad absorbed i partile-like pakages of defiite disrete amout of eergy, alled photos. The eletro of the metal iterats with oe photo of light as if the eletro had bee struk by a partile. Yet a photo has wave-like harateristis beause its eergy is proportioal to the frequey of the radiatio: E = hf : h = Js The questio, Is light a wave or a partile? is iappropriate beause light propagatio ad of the effets of iterferee are best desribed by wave model, whereas the photoeletri effet ad other experimets ivolvig the iteratio of light with matter require a partile approah. 8. Measuremet of the speed of light The speed of light i vauum is = m/s. Sie the mea radius of the Earth = m, light takes less tha a seod to make roud trip about the Earth!

2 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - The speed is so large that it was thought to travel istataeously. Fizeau s Tehique Let d is the distae betwee soure ad mirror. If the trasit time for o roud trip is t, the d the speed of light is. t To measure the trasit time t, Fizeau used a toothed wheel rotated at ostat agular speed. Let the wheel has N equally spaed othes. The agle betwee othes is. N d The time for the wheel to rotate from the first oth (where the light passes the wheel to the mirror) to the d oth (where the light returs from the mirror) is t. Rotatig toothed wheel With, t Nt, we get d t d N dn. Example : Assume Fizeau s wheel has 360 teeth ad is rotatig at 7.5 rev/s. A burst of light passig through a oth is bloked by adjaet tooth o retur. If the distae to the mirror is 7500 m, fid the speed of light. I the time t the light makes its roud trip, the wheel turs through a agle From the defiitio of agular speed, we see the time t is ( / 70) rev 5 t s. 7.5 rev/s Hee, the speed of light is d (7500m) 5 t s m/s of /70 rev. 8.3 Refletio ad Refratio Refletio Whe a light travelig i a medium eouters a boudary leadig ito a seod medium, part or all of the iidet s are refleted bak ito the first medium.

3 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 3 If the refletig surfae is smooth, the refleted s are parallel to eah other; a speular refletio. If the refletig surfae is rough, the s are refleted i various diretios, ad it is kow as diffuse refletio. Iidet Normal i r Refleted Law of refletio: i = r The iidet, the refleted, ad the ormal all lie i the same plae The agles are always measured from the ormal, whih is defied to be a lie perpediular to the surfae of the plae. Example : Two mirrors make a agle of 0 with eah other. A is iidet o mirror M at a agle of 65 to the ormal. Fid the diretio of the after it is refleted from mirror M. M M From the law refletio, the seod refleted makes a agle of 55 with the ormal to M Refratio Whe a light travelig i a trasparet medium eouters a boudary leadig ito aother trasparet medium, part of the, if ot all, is refleted ad part eters the d medium. The that eters the d medium is bet at the boudary ad is said to be refrated. All s ad the ormal lie i the same plae. Iidet Normal r Refleted Law of refratio, whih is geerally kow as Sell s Law: si = si All s ad the ormal lie i the same plae. Air Glass Refrated : the speed of light i vauum v: the speed of light i the material The quatities ad are the refrative idies of media ad, respetively. The refrative idex (or the idex of refratio) of a material is defied as (always > ) v The greater the idex refratio, the slower the wave speed i that material.

4 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 4 As the light travels from oe medium to aother, both the wave speed ad the wavelegth do hage but the frequey does ot hage. The boudary surfae aot reate or destroy waves. That is the umber of wave yles arrivig per uit time must equal umber of wave yles leavig per uit time. Otherwise, the waves will pile up i oe of the media. Alteratively the refrative idex a be writte as v f f o o The figure shows that the idex of refratio of material is ot ostat, but varies with the wavelegths of the light. It geerally dereases with ireasig wavelegth. So, violet light beds more tha red light whe passig ito a refratig material Note: Refrative idex of air is , m Example 3: A beam of light of = 550 m travelig i air is iidet o a slab of trasparet material. The iidet beam makes a agle of 40.0, ad the refrated beam makes a agle of 6.0 with the ormal. Fid the idex of refratio of the material. From Sell s law: si = si si si si 40.0 (.00) si Exerise: What is the frequey of light i the material? Aswer: Hz Example 4: Light of wavelegth 589 m i vauum passes through a piee of silia ( =.458). Fid the wavelegth ad the speed of light i silia. The wavelegth of the light i silia, The speed of light i silia, v o m m m/s Exerise : A light- of wavelegth = 589 m travelig through air is iidet o a smooth, flat slab of row glass (refrative idex.5) at a agle of 30.0 to the ormal. What is the agle of refratio? What is the wavelegth of the light iside the glass? What is the frequey of the light iside the glass? Aswer: 9., m, Hz. Exerise : The atual depth of a shallow pool.0 m deep is ot the same as the apparet depth see whe you look straight dow at the pool from above. How deep (i m) will it appear to be? ( water =.33) Aswer: 75

5 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis Total Iteral Refletio Normal Refrated s Iidet s Refleted s We have desribed how light is partially refleted ad trasmitted at the iterfae betwee two media with differee idexes of refratio. All the light, however, a be totally refleted whe the light propagates from a optially deser medium (higher ), ad if the agle of iidee is greater tha the ritial agle,. The agle of iidee for whih the refrated emerges taget to the surfae is alled the ritial agle. We a use Sell s law of refletio to fid the ritial agle. Whe 90,, si si Sell s law gives si si 90 si will be small whe is osiderably larger tha. Examples of this ombiatio are diamod ( =.4 ad = 4 ) ad row glass ( =.5 ad = 4 ) i iterfae with air (.00). Whe total iteral refletio ours the iterfae ats as a perfet refletor; o light is refrated. Commo appliatios of total iteral refletio are i bioulars, submarie perisope. The agles of iidee o the sides of the prism are all 45, whih is greater tha the ritial agle for row glass at a air-glass iterfae Total iteral refletio eables light to be trasmitted iside thi glass fibers. The light is iterally refleted off the sides of the fiber, ad, therefore, follows the path of the fiber. Light a atually be trasmitted aroud orers usig a glass fiber, provided that the beds i the fiber are ot too sharp, so that the light always strikes the sides of the fiber at agles greater tha the ritial agle. The whole field of fiber optis, with its may useful appliatios, is based o this effet.

6 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 6 Example 5: A view from the fish s eye (a) Fid the ritial agle for a water-air boudary if the idex of refratio of water is.33. si (b) Predit what a fish sees whe it looks upwards toward the water surfae at a agle of 40, 49, ad 60. At 40 (< ), the fish a see out of the water. At 49 ad 60 (> ), the fish sees a refletio of some objet o the bottom of the pool. Exerise: A layer of ethyl alohol ( =.36) is o top of water ( =.333). At what miimum agle relative to the ormal to the iterfae of the two liquids is light totally refleted? Aswer: 78.36