h o h d Angular magnification Angular magnification of a magnifying glass

Transcription

1 6. Angular Magniicatin an the Magniying Glass Angular magniicatin M θ The reerence angular size θ is base n nrmal reaing/viewing at istance N (either ~5 cm r the near pint istance): θ θ h N The magniie angular size θ is base n the ray trace rm the center the lens, thrugh the tip the bject, t the tip the virtual image θ ' hi i h Angular magniicatin a magniying glass M N i N The user etermines the angular magniicatin by varying the bject istance (but keeping i >N i arsighte)

2 6. The Cmpun Micrscpe T increase the angular magniicatin beyn that pssible with a magniying glass, an aitinal cnverging lens can be inclue t pre-magniy the bject. L L istance between lenses (3) Height the bject r the eyepiece: (4) Image angular size: (5) Cmpare t riginal angular size: θ () Linear magniicatin M the bjective lens is therere: h θ ' h N h i i ( L e ) e h h e Basic perating principle: () Ajust bject istance such that the real, inverte image lies just insie the cal pint the eye piece: ( L ) ( L h M Angular magniicatin a cmpun micrscpe e ) h M i θ θ ' i ( L e ) ( L ) e e e N

3 Chapter 7 Intererence an the Wave Nature Light 3

4 7. The Principle Linear Superpsitin When tw r mre light waves pass thrugh a given pint, their electric (an magnetic) iels cmbine (interere) accring t the principle superpsitin. Special Case Special Case The waves emitte by the surces start ut in phase an arrive at pint P in phase, leaing t cnstructive intererence. m m 0,,,3, The waves emitte by the surces start ut in phase an arrive at pint P in ppsite phase, leaing t estructive intererence. m ( m + ) 0,,,3, I cnstructive r estructive intererence is t cntinue curring at a pint, the surces the waves must be cherent surces. Tw surces are cherent i the waves they emit maintain a cnstant phase relatin. 4

5 7. Yung s Duble Slit Experiment Tw inepenent, cherent light surces are virtually impssible t cnstruct. In Yung s experiment (Yung als participate in the eciphering the Rsetta Stne), tw slits illuminate by a single surce acts as tw separate but cherent surces light. Light waves rm these slits interere bth cnstructively an estructively n the prjectin screen. Fr best results, light a single clr (e.g. pruce by a laser) is use. The waves cming rm the slits interere cnstructively r estructively, epening n the ierence in istances between the slits an the screen. 5

6 7. Yung s Duble Slit Experiment In the typical set up, the screen is very ar away cmpare t the separatin the slits. We treat the rays rm the slits as i they were parallel Bright ringes rm slits sinθ m Bright ringes Dark ringes sinθ sinθ m sinθ ( m + ) m 0,,,3, Dark ringes rm slits Bright ringe Dark ringe ( m ) sin + θ m Bright ringe Dark ringe Bright ringe 6

7 7. Yung s Duble Slit Experiment Example: Yung s Duble-Slit Experiment Re light (664 nm) is use in Yung s experiment with slits separate by m. The screen is lcate a istance.75 m rm the slits. Fin the istance n the screen between the central bright ringe an the thir-rer bright ringe. θ m sin m sin m 0.95 (.75 m) tan( 0.95 ) m y L tan θ Nte: Duble slit intererence als separates ut the clrs rm a white r multi-clre surce. The angle the bright ringes is ierent r each wavelength the bright ringes r ierent clrs rm a rainbw n screen. 7

8 7.3 Thin Film Intererence Because relectin an reractin, (at least) tw light waves enter the eye when light shines n a thin ilm gasline lating n a thick layer water. Because the extra istance travele by ray [] relative t ray [], there can be intererence between the tw waves. Fr the cmparisn the extra path t wavelength, we nee t use the wavelength in the meium ilm n vacuum ilm When light travels thrugh a material with a smaller reractive inex twars a material with a larger reractive inex, (partial) relectin at the bunary ccurs alng with a phase change that is equivalent t ne-hal a wavelength in the ilm. When light travels rm a larger twars a smaller reractive inex, there is n phase change upn relectin. 8

9 7.3 Thin Film Intererence Example Clr a Thin Film Gasline A thin ilm gasline lats n a pule water. Sunlight alls perpenicularly n the ilm an relects int yur eyes. The ilm has a yellw hue because estructive intererence eliminates the clr blue (469 nm) rm the relecte light. The reractive inices the blue light in gasline an water are.40 an.33. Determine the minimum nn-zer thickness the ilm. Ray []: relectin at pint A rm lwer t higher inex: phase shit equivalent t ½ ilm ilm A B Ray []: relectin at pint B rm higher t lwer n phase shit ; but runtrip thrugh ilm: t Eective path ierence between Ray [] an Ray [] (incluing phase shit r relectin) t ilm Destructive intererence between Ray [] an Ray []: ierence hal-integer wavelengths t ilm, ilm, 3ilm... t ilm, 3 ilm ilm, 5 ilm... Minimum nn-zer thickness t : t 469 nm.40 ilm 68 nm 9

10 7.3 Thin Film Intererence The wege air rme between tw glass plates causes an intererence pattern alternating ark an bright ringes. Thin-ilm ban-pass ptical ilter y Dark Fringes y ( m + ) m 0,,,3 Bright Fringes... m As lng as the ilm has the highest reractive inex the three regins, then neither the tw relectins incur a phase shit. t Cnstructive intererence between transmitte ray [] an ray [] ccurs r the minimum thickness t ilm 0

11 7.5 Diractin In the -slit intererence pattern, the alternating bright an ark ringes appears t be mulate by a larger scale structure These are the result the inite with the slits Using a single slit the same with, we can pruce a pattern that cnsists just the mulating envelpe nly This single-slit pattern is ue t the iractin light Diractin reers t the bening waves arun bstacles r the eges an pening. Huygens principle Every pint n a wave rnt acts as a surce tiny wavelets that mve rwar with the same spee as the wave; the wave rnt at a latter instant is the surace that is tangent t the wavelets.

12 7.5 Diractin This tp view shws the rays r ive surces Huygens wavelets. Wave rnts rm all ive arrive in phase at the central maximum (bright ringe) First Dark Fringe: wavelets rm,3,5 arrive successively separate by hal wave-length: Destructive intererence Wavelets rm,4 als arrive separate by hal wave-length. This ccurs at Wsinθ

13 7.5 Diractin Secn Dark Fringe: wavelets rm,,3,4, an 5 arrive successively separate by hal wavelength: Destructive intererence This ccurs at Wsinθ Dark ringes r single slit iractin sin θ m m,,3, W Fr higher rer ark ringe, we nee t break the slit up int mre surces Nte that the m0 case here crrespns t the central maximum 3

14 7.7 The Diractin Grating An arrangement cnsisting a large number clsely space, parallel slits is calle a iractin grating. The multiple slits enhances the cnstructive intererence at the maxima (bright ringes) the -slit case (with the same slit spacing ) 4

15 7.7 The Diractin Grating The bright ringes pruce bya iractin grating are much narrwer than thse pruce by a uble slit. Principal maxima a iractin grating sin θ m m 0,,,3, istance between ajacent slits Reversing this equatin sinθ m This technique allws ne t make very precise measurements the wavelength Heate atms emit characteristic wavelengths. The Emissin (absrptin) wavelength pattern is calle the emissin (absrptin) spectrum The element helium (He) was riginally iscvere by its spectrum in sunlight. 5

16 7.7 The Diractin Grating Example: Separating Clrs With a Diractin Grating A mixture vilet (40 nm) light an re (660 nm) light alls nta grating that cntains.00x0 4 lines/cm. Fr each wavelength, in the angle that lcates the irstrer maximum cm.00 0 cm m vilet (40 nm) re (660 nm) θ θ 9 vilet 40 0 m sin sin m 9 re m sin sin m