Physics 30 Lesson 8 Refraction of Light

Transcription

1 Physis 30 Lesso 8 Refratio of Light Refer to Pearso pages 666 to 674. I. Refletio ad refratio of light At ay iterfae betwee two differet mediums, some light will be refleted ad some will be refrated, exept i ertai ases whih we will soo disoer. Whe problem solig for refratio, we usually igore the refleted ray. Glass prism II. Idex of refratio The fastest that light a trael is i a auum ( = 3.00 x 0 8 m/s). I other substaes, the speed of light is always slower. The idex of refratio is a ratio of the speed of light i auum with the speed of light i the medium: speed i auum () idex of refratio () speed i medium () = Some ommo idies of refratio are: Substae Idex of refratio () auum.0000 air.0003 water.33 ethyl alohol.36 quartz (fused).46 glyerie.47 Luite or Plexiglas.5 glass (row).5 sodium hloride.53 glass (rystal).54 ruby.54 glass (flit).65 ziro.9 diamod.4 Notie that the idex of refratio () is always greater tha or equal to ad that it has o uits. Dr. Ro Liht 8

2 Example The idex of refratio for row glass was measured to be.5. What is the speed of light i row glass? ms m s III. Law of Refratio (Sell's Law) Refratio is the hage i speed, waelegth ad diretio of light aused by a hage i medium. For example, whe light passes from air ito water, the speed dereases, the waelegth dereases, ad the light ray beds i toward the ormal. ormal - agle of iidee Iidet ray i,, - agle of refratio,, Refrated ray r Dr. Ro Liht 8

3 I 6, Willebrord Sell, a Duth mathematiia, determied the relatioship betwee the agles, waelegths ad speeds of refrated waes. These relatioships are referred to as Sell s law or the Law of Refratio. We will ow derie Sell s law. The diagram represets a wae traellig from a fast medium ito a slow medium. 90 o agle,, f From the iidet triagle we get si hypoteuse,, f From the refratio triagle we get si hypoteuse ommo hypoteuse 90 o agle Diidig the equatios we get We hae si si si si Usig the uiersal wae equatio si si f f hypoteuse hypoteuse f we a derie aother relatioship: f For light we also hae aother relatioship that we a ilude. Sie ad the si si Sell s Law (i.e. The Law of Refratio) is: si si ad we a use ay pairig that we desire. Dr. Ro Liht 8 3

4 Example If light has a agle of iidee of 30 o whe traellig from air ito water, what is the agle of refratio? si 30 o si si si air water si si o si.00 si30.33 Example 3 If light has a agle of iidee of 30 o whe traellig from water ito air, what is the agle of refratio? si si 30 o si si water air.33 si30 si.00 Example 4 o 4.9 If light has a agle of iidee of 30 o ad a agle of refratio of 6 o whe traellig from water ito substae X, what is the idex of refratio for X? water X 30 o si si.33 si30 si6.5 6 o Example 5 If the speed of light i air is 3.00 x 0 8 m/s, what is the speed of light i glass ( glass =.50)? 8.00( ms ) m s Dr. Ro Liht 8 4

5 Example 6 If light has a waelegth of 750 m i air, what is the waelegth of light i diamod ( diamod =.4)? IV. Speial problems.00(750m).50 30m A. Parallel sides origial ray exteded Whe light passes through a medium with parallel sides, the origial agle of iidee always equals the fial agle of refratio. The iteral agles are also the same. Note that the origial ray is parallel with the emergig ray. 70 o 38 o 38 o 70 o emergig ray air B. Triagular prisms air plate glass widow pae A lassi problem is whe light refrats through a triagular prism. Sie the sides are ot parallel, the iteral agles of refratio ad iidee will ot be the same. Example 7 If light eters a equilateral glass prism ( =.50) with a agle of iidee of 45 o, what is the agle of refratio as the beam emerges from the prism? Note that a equilateral triagle has three 60 o agles. si =.00 si 45 o.50 = 8. o = 90 o - = 90 o - 8. o = 6.88 o 3 = 80 o - (60 o + ) = 80 o -.88 o = 58. o 4 = 90 o - 3 = 90 o o = 3.88 o si 5 =.50 si 3.88 o.00 5 = 5.4 o Dr. Ro Liht 8 5

6 V. Total iteral refletio Refer to Pearso pages 67 to 674. Whe a light ray passes from a more optially dese medium (high, low ) to a less optially dese medium (low, high ), the agle of refratio ( r ) is greater tha the agle of iidee ( i ). Low High i r As the agle of iidee is ireased, the agle of refratio beomes larger util fially r approahes 90 o. Low High i r At the agle of iidee alled the ritial agle ( ) the agle of refratio = 90 o. Low r = 90 o High At agles beyod the ritial agle, refratio a o loger our the result is total iteral refletio whih obeys the law of refletio. I other words, at agles beyod the ritial agle the boudary betwee the media ats as a mirror surfae. Low (high speed) High (low speed) i r = i Total iterally refleted light ray The properties of iteral refletio are used i fibre opti tehologies ad i optial istrumets like ameras, mirosopes, bioulars, et. Note that total iteral refletio ours oly whe light traels from low to high speed media. It does ot our whe light traels from high to low speed media. Dr. Ro Liht 8 6

7 Example 8 What is the ritial agle for a water ad air iterfae? For the ritial agle = 90 o si si : si si.00 si90 si.33 o 48.8 Example 9 If light makes a agle of iidee of 60 o whe traellig from diamod ito water, what is the agle of refratio produed? si.4si60 si.33 error si VI. Pratie problems Note that this error result does ot idiate that you hae made a mistake i alulatio. The result meas that o refratio is possible resultig i total iteral refletio.. A ray of light has a agle of iidee of 4 o from air ito water. What is the agle of refratio? (Refer to the table of refratie idies at the begiig of this lesso.) (7.8 o ). A light ray is traellig from row glass ito air. The agle of iidee is 0 o. What is the agle of refratio? (3.3 o ) Dr. Ro Liht 8 7

8 3. The agle of refratio i air is 60 o. Fid the agle of refratio i the water. ( plasti =.5) (40.6 o ) air plasti water 4. For the followig prism ( =.50) fid the idiated agle if the agle of iidee is 40 o. (38.7 o ) 50 o? 5. To suessfully spear a fish, you must aim below the apparet positio of the fish. Explai. Dr. Ro Liht 8 8

9 6. What is the ritial agle whe light emerges from glass ( =.50) ito air? (4.8 o ) 7. The ritial agle betwee glass ad water is 56. o. What is the idex of refratio for the glass? (.60) 8. The agle of refratio i water is 60 o. If plasti =.6 trae the ray path through the system below. water plasti air VII. Had-i assigmet. The speed of light i a ertai plasti is.0 x 0 8 m/s. What is the refratie idex of the plasti? (.5). The idex of refratio of row glass for iolet light is.53. ad for red light.5. Assumig that the eloity of light i a auum is 3.00 x 0 8 m/s, what are the speeds of iolet light ad red light i row glass? (.96 x 0 8 m/s,.97 x 0 8 m/s) 3. A beam of light strikes the surfae of water with a iidet agle of 60 o. Some of the light reflets off the water ad some refrats ito the water. If water has a idex of refratio of.33, determie the agles of refletio ad refratio. (60 o, 4 o ) Dr. Ro Liht 8 9

10 4. A wae traellig from air to glass =.5) has a agle of iidee of 30 o. What is the agle of refratio? (9 o ) 5. If the agle of iidee is 0 o ad the agle of refratio is 0 o, what is the idex of refratio of the material if the wae started i air? (.97) 6. What is the waelegth of light i water if the waelegth i air is 570 m? (49 m) 7. A ray of light eters from air to water ad the ito glass as show i the diagram. Fid the agle of refratio i glass. ( water =.33, glass =.50) (33 o ) 35 o air water glass 8. Light strikes the 70 o glass prism ( =.5) with a agle of iidee of 50.0 o. Calulate the agle that the light leaes the prism. (73.9 o ) 70 o? 9. Light is iidet o a equilateral Luite prism ( =.5) at a agle of 35 o. Calulate the agle that the light leaes the prism. (66 o )? 0. Freddie the fish shies his flashlight upward from uder water. A. If Freddie shies his flashlight at a iidet agle of 0 o, at what agle does the light leae the water? (7 o ) B. Beyod what ritial agle will the light o loger be able to leae the water? (48.8 o ). From iside a aquarium a ray of light is direted at the glass so the agle of iidee, i water, is 30 o. (a) Determie the agle of refratio whe the ray emerges from the glass ito the air. (b) If the agle of iidee i the water is 5 o at what agle will the rays emerge from the glass? (4 o, o ray emerges) water = o air =.00 glass =.50 Dr. Ro Liht 8 0

11 . A uderwater swimmer looks up toward the surfae of the water o a lie of sight that makes a agle of 5 o with a ormal to the surfae of the water. What is the agle of iidee i air for the light rays that eter the swimmer's eyes? (34 o ) 3. You tape a pey to the iside bottom of a up ad moe your eye away from the up to just that poit where you a o loger see the pey oer the rim of the up. If someoe slowly adds water to the up, the pey omes ito iew. Usig diagrams ad a word desriptio, explai why. (Peies ad styrofoam ups are aailable. Seeig is belieig! Try it!) 4. Hot air rises oer a heated stoe elemet. Explai why the wall behid the stoe appears to shimmer. 5. The ritial agle from rok salt ito air is 40.5 o. What is the idex of refratio for rok salt. (.54) 6. The ritial agle for a ertai liquid-air surfae is 6 o. What is the liquid's idex of refratio? (.4) 7. The refratie idies of diamod ad row glass are 5/ ad 3/ respetiely. What is the ritial agle betwee diamod ad glass? (37 o ) 8. A ray of light eters AC alog the ormal. Trae the subsequet ray path. ( =.50) A 45 o B C 9. A bright poit soure of light is plaed at the bottom of a 0 m deep pool of water, =.33. What is the area of the irle of light whih is see at the surfae of the water? What happeed to the other light rays? (634 m ) 0. A studet performs a experimet where she measures the agles of iidee ad refratio for a partiular type of glass. She obtais the followig results: agle of agle of iidee refratio 0 o 0 o 0 o 6 o 0 o o 30 o 8 o 40 o 3 o 50 o 8 o 60 o 3 o Usig a appropriate graphig tehique, alulate the idex of refratio for the glass. Dr. Ro Liht 8

12 Atiity Idex of Refratio Proedure:. Workig with oe parter, plae a piee of paper o the table ad plae the retagular prism as show i the diagram below. With a peil, trae aroud the retagular prism. The draw a lie that meets the retagular prism at a agle of iidee of 50 o. Top View lie 8 x paper Retagular prism. Plae the laser poiter so that the light rus dow the peil lie. Look for the emerget ray as it leaes the prism ad draw a peil lie for the emerget ray. 3. Draw i the ray path through the prism. 4. At the poit where light eters the prism draw i a ormal to the prism surfae. Usig a protrator measure the agle of iidee ad the agle of refratio at the iterfae. 5. Calulate the idex of refratio for the retagular prism. Dr. Ro Liht 8

13 Atiity Equilateral Triagle Prism Proedure:. Workig with oe parter, plae a piee of paper o the table ad arrage a equilateral triagle prism as show i the diagram below. With a peil, trae aroud the prism ad draw a lie as show. Top View 8 x paper Equilateral prism lie. Plae the laser poiter so that the light rus dow the peil lie. Look for the emerget ray as it leaes the prism ad draw a peil lie for the emerget ray. 3. Draw all of the resultig ray paths iludig the rays through the prism ad those refleted from ad withi the prism. 4. For eah ray, explai how ad why the ray is emergig where it is. Dr. Ro Liht 8 3

14 Atiity 3 Equilateral Triagle Prism (Total Iteral Refletio) Proedure:. Workig with oe parter, plae a piee of paper o the table ad arrage a equilateral triagle prism as show i the diagram below. With a peil, trae aroud the prism. Use a protrator to draw a lie at 90 o to the prism fae. (Note: Make sure that you do ot draw the lie from the etre of the fae of the triagular prism. The lie should be offset from etre.) Top View 8 x paper Equilateral prism. Poit the laser poiter diretly dow the lie. Draw a peil lie i for the emerget ray. 3. Draw i the ray path through the prism. Explai the resultig ray path. Dr. Ro Liht 8 4

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