Chapter 35 - Refractio A PowerPoit Presetatio by Paul E. Tippes, Professor of Physics Souther Polytechic State Uiersity 2007
Objecties: After completig this module, you should be able to: Defie ad apply the cocept of the idex of refractio ad discuss its effect o the elocity ad waelegth of light. Apply Sell s s law to the solutio of problems iolig the refractio of light. Determie the chages i elocity ad/or waelegth of light after refractio. Defie ad apply the cocepts of total iteral reflectio ad the critical agle of icidece.
Refractio Refractio is is the bedig of of light as it it passes from oe medium ito aother. Note: the agle of icidece A i air ad the agle of refractio A i water are each measured with the ormal N. A w N Water refractio The icidet ad refracted rays lie i i the same plae ad are reersible.
Refractio Distorts Visio Water Water The eye, belieig that light traels i i straight lies, sees objects closer to to the surface due to to refractio. Such distortios are commo.
The Idex of Refractio The idex of of refractio for a material is is the ratio of of the elocity of of light i i a acuum (3 x 10 8 m/s) to to the elocity through the material. Idex of refractio c c c Examples: = 1; 1; glass = 1.5; Water = 1.33
Example 1. Light traels from air ( ( = 1) ) ito glass, where its elocity reduces to oly 2 x 10 8 m/s. What is the idex of refractio for glass? air = c Glass G = 2 x 10 8 m/s c 8 3 x 10 m/s 8 2 x 10 m/s For glass: = 1.50 If the medium were water: W = 1.33.. The you should show that the elocity i water would be reduced from c to 2.26 x 10 8 m/s.
Aalogy for Refractio 3 x 10 8 m/s Paemet Glass 2 x 10 8 m/s Sad s < p 3 x 10 8 m/s Light beds ito glass the returs alog origial path much as a rollig axle would whe ecouterig a strip of of mud.
Deriig Sell s s Law Cosider two light rays. Velocities are 1 i medium 1 ad 2 i med. 2. Segmet R is commo hypoteuse to two rgt. triagles. Verify show agles from geometry. si t R ; si t R 1 2 1 2 1 Medium 2 2 t 1 2 R Medium 1 1 t t si R si t R 1 1 1 2 2 2
Sell s s Law Medium 1 1 2 1 Medium 2 2 The ratio of of the sie of of the agle of of icidece 1 to to the sie of of the agle of of refractio 2 is is equal to to the ratio of of the icidet elocity 11 to to the refracted elocity 22. Sell s Law: si si 1 1 2 2
Example 2: A laser beam i a darkeed room strikes the surface of water at a agle of 30 0. The elocity i water is 2.26 x 10 8 m/s. What is the agle of refractio? 30 0 A The icidet agle is: A = 90 0 30 0 = 60 0 H 2 O W si A si W A W 8 0 W si A (2 x 10 m/s)si 60 siw W = 35.3 0 A 8 3 x 10 m/s
Sell s s Law ad Refractie Idex Aother form of Sell s s law ca be deried from the defiitio of the idex of refractio: 1 Medium 1 2 Medium 2 c from which c ; c 1 1 1 2 2 2 1 2 c Sell s s law for elocities ad idices: si si 1 1 2 2 2 1
A Simplified Form of the Law Sice the idices of refractio for may commo substaces are usually aailable, Sell s s law is ofte writte i the followig maer: si si 1 1 2 2 2 1 si si 1 1 2 2 The product of of the idex of of refractio ad the sie of of the agle is is the same i i the refracted medium as for the icidet medium.
Example 3. Light traels through a block of glass, the remerges ito air. Fid agle of emergece for gie iformatio. First fid G iside glass: 50 0 Glass G G =1.5 si si A A G G Asi A (1.0)si 50 sig 1.50 G G = 30.7 0 0 From geometry, ote agle G same for ext iterface. Apply to e each iterface: = 50 0 Same Asi A GsiG Asi as etrace agle! A
Waelegth ad Refractio The eergy of light is determied by the frequecy of the EM waes, which remais costat as light passes ito ad out of a medium. (Recall = f.) f Glass =1 A =1.5 G f A = f G G A f ; f A A A G G G A fa A A ; ; f G G G G si si 1 1 1 2 2 2
The May Forms of Sell s s Law: Refractio is is affected by the idex of of refractio, the elocity, ad the waelegth. I geeral: Sell s Law: si si 1 2 1 1 2 1 2 2 All the ratios are equal. It It is is helpful to to recogize that oly the idex differs i i the ratio order.
Example 4: A helium eo laser emits a beam of waelegth 632 m i air (( A = 1). 1 What is the waelegth iside a slab of glass ( ( G = 1.5)? Glass G G =1.5 G = 1.5; A = 632 m A G AA ; G G A G G (1.0)(632 m) 1.5 421 m Note that the light, if see iside the glass, would be blue.. Of course it still appears red because it returs to air before strikig the eye.
Dispersio by a Prism Red Orage Yellow Gree Blue Idigo Violet Dispersio is is the separatio of of white light ito its arious spectral compoets. The colors are refracted at at differet agles due to to the differet idexes of of refractio.
Total Iteral Reflectio Whe light passes at a agle from a medium of higher idex to oe of lower idex, the emergig ray beds away from the ormal. light c 90 0 Critical agle i = r Water Whe the agle reaches a certai maximum, it will be reflected iterally. The critical agle c is is the limitig agle of of icidece i i a deser medium that results i i a agle of of refractio equal to to 90 0.
Example 5. Fid the critical agle of icidece from water to air. For critical agle, A = 90 0 A = 1.0; W = 1.33 si si W C A A A sic 0 si 90 (1)(1) w 1.33 Critical agle Critical agle: c = 48.8 0 Water c 90 0 I geeral, for media where 1 > 2 we fid that: si C 1 2
Summary Medium c = 3 x 10 8 m/s Idex of refractio c Refractio is is affected by the idex of of refractio, the elocity, ad the waelegth. I geeral: Sell s Law: si si 1 2 1 1 2 1 2 2
Summary (Cot.) The critical agle c is is the limitig agle of of icidece i i a deser medium that results i i a agle of of refractio equal to to 90 0. Critical agle 2 c 90 0 1 1 > 2 I geeral, for media where 1 > 2 we fid that: si C 1 2
CONCLUSION: Chapter 35 Refractio