PHYS 450 Spring semester Lecture 06: Dispersion and the Prism Spectrometer. Ron Reifenberger Birck Nanotechnology Center Purdue University

Size: px

Start display at page:

Download "PHYS 450 Spring semester Lecture 06: Dispersion and the Prism Spectrometer. Ron Reifenberger Birck Nanotechnology Center Purdue University"

Denis Ellis
5 years ago
Views:

$Exploited by Newto betwee 666 ad 67 si i ( i s ) r The refractive idex of a glass prism is greater for$

1 /0/07 PHYS 450 Sprig semester 07 Lecture 06: Dispersio ad the Prism Spectrometer Ro Reifeberger Birck Naotechology Ceter Purdue Uiversity Lecture 06 Prisms Dispersio of Light As early as the 3th cetury, accouts of six-sided crystals of atural quartz used to geerate raibows. Exploited by Newto betwee 666 ad 67 si i ( i s ) r The refractive idex of a glass prism is greater for violet light, smaller for red light.

$/0/07 Prism Fudametals A prism is a trasparet optical elemet with flat, polished surfaces that refracts light. At least two of the flat surfaces must have a agle betwee them.$ $Apex. Base 3. Refractig agle, Apex agle 4. Agle of deviatio A prism causes o-moochromatic light to disperse 4$

2 /0/07 Prism Fudametals A prism is a trasparet optical elemet with flat, polished surfaces that refracts light. At least two of the flat surfaces must have a agle betwee them. Light i Apex Agle α Light out Prism Fuctio: Dispersio Beam steerig Beam maipulatio Polarizatio alterig Beamsplittig Base 3 Prism Compoets ad Fuctio Apex Agle α Three Importat Properties of a Prism Light i δ Light out A prism deviates light without chagig the curvature of the optical wavefrot, i.e. the emergig light is ot focused/defocused A prism obeys Sell s Law ad displaces the light beam toward the base Base. Apex. Base 3. Refractig agle, Apex agle 4. Agle of deviatio A prism causes o-moochromatic light to disperse 4

/0/07 i) Prisms bed light without focusig Importat Properties ii) The agle of deviatio does ot deped where the light hits the surface of a prism (IMPORTANT) δ Simulatios from https://phet.colorado.

3 /0/07 i) Prisms bed light without focusig Importat Properties ii) The agle of deviatio does ot deped where the light hits the surface of a prism (IMPORTANT) δ Simulatios from light/latest/bedig light_e.html 5 Importat Properties (cot.) iv) Beam splittig applicatio v) Chage Agle of light beam 44 o 40 o Light ray thru prism becomes parallel to base 47 o 6 3

/0/07 BEWARE - iteral reflectios ca be a issue!

AmaterialpropertyofglassesistheAbbe umber, which quatifies the amout of dispersio that

$It is a fuctio of the refractive idex of a material at three well-defied wavelegths: f$

4 /0/07 BEWARE - iteral reflectios ca be a issue! Moochromatic light 7 Dispersio of EM Wave: varies with H He H f d c AmaterialpropertyofglassesistheAbbe umber, which quatifies the amout of dispersio that a glass exhibits. It is a fuctio of the refractive idex of a material at three well-defied wavelegths: f (486.m), d (587.6m), ad c (656.3m). The Abbe umber is defied as Values of Abbe umber rage from Crow glasses have v d > 50 (less dispersive) Flit glasses with v d < 50 (more dispersive) ca be measured 8 4

9 Schematic The Prism Spectrometer - Basic Idea Top View A B C D http://www.chemistrylad.

5 /0/07 The Glass Map PRISMS LENSES Desigatios that ed i K refer to a crow glass. Those that ed i F refer to flit glass. 9 Schematic The Prism Spectrometer - Basic Idea Top View A B C D Atomic%0Structure/Spectra/ModerAtom5.html A. Slit B. Collimator Les C. Dispersig Prism D. Telescope Objective E. Positio of Cross Hairs F. Eyepiece Les G. ½-silvered Diagoal Mirror H. Eyepiece Les F E G H 0 5

/0/07 Gas Discharge Tube - Discrete Wavelegths (Ågström 868: 000 spectral lies, Swede) Spectral Lies for Commo Gases http://www.

html H He Hg Glass tube, evacuated ad backfilled to low pressure with a gas like hydroge, helium, eo, etc. U https://www.reddit.

6 /0/07 Gas Discharge Tube - Discrete Wavelegths (Ågström 868: 000 spectral lies, Swede) Spectral Lies for Commo Gases Atomic%0Structure/Spectra/ModerAtom5.html H He Hg Glass tube, evacuated ad backfilled to low pressure with a gas like hydroge, helium, eo, etc. U Top View Prism Spectrometer Top View Cautio: high voltage =agle of deviatio See Appedix for discussio of a Verier scale 6

/0/07 America Optical Prism Spectrometer eye telescope prism piece collimator adjustable table slit focus Telescope

distat object usig large brass Focus Adjust kob c) move the telescope eyepiece i/out util the cross hairs come ito

of ~½ mm usig slit adjustig kob g) view the slit through the telescope, the slit should appear to be focused h) alig

paralleltoslit,makesuretheverier zero is aliged with the 360 o /0 o mark o the circular scale j) isert prism ad offset

7 /0/07 America Optical Prism Spectrometer eye telescope prism piece collimator adjustable table slit focus Telescope Lock Verier Lock Use with He discharge lamp ad measure () for ~0 lies ALIGNMENT a) remove prism b) focus telescope o distat object usig large brass Focus Adjust kob c) move the telescope eyepiece i/out util the cross hairs come ito focus; d) oriet cross hairs by rotatig telescope tube e) poit telescope directly at collimator f) ope slit to a width of ~½ mm usig slit adjustig kob g) view the slit through the telescope, the slit should appear to be focused h) alig the vertical cross hair with the log axis of the slit i) with the vertical cross hair aliged paralleltoslit,makesuretheverier zero is aliged with the 360 o /0 o mark o the circular scale j) isert prism ad offset ~ cm from telescope/collimator axis 3 Two Importat Quatities A. Agle of deviatio δ B. Resolvig Power, two closely spaced wavelegths Two wavelegths: = -Δ & 4 7

8 /0/07 A. Calculatig the agle of deviatio Experimetally, all you ca cotrol is θ i a si i si t Apex Iterface δ=δ +δ b si i si t i t t i t i i t t i t i (i) (ii) (iii) (iv) (v) θ i P δ δ θ t Q θ i θ t R Iterface What is δ?? air prism Base 5 from b t i si t : si si si si si cos cos si si t t t t si si cossi t si si t cos si t t it ow use a i i c t si si si cos s si si si cos si from v Workig it out goal is to write δ( i ) : t trig idetity si i si si i cossi i ow move iside sqrt Mai Result A 6 8

9 /0/07 i i Very complicated! Simplify? small agle approximatio for δ isi si si cos si exact, but ugly for i, sii i for, si, cos isi i i 0.0% -.0% -4.0% i si -6.0% -8.0% -0.0% i si... i si... i... i Light with highest idex approximate of refractio beds most [(si(φ)-φ)/si(φ)] x 00% Percet Error i Small Agle Approximatio Agle φ (i degrees) 7 Plot δ vs. θ i i si si si i cos si i t Plot θ t / θ i vs. θ i i i si si si cos si i i δ mi Agle of miimum deviatio 8 9

10 /0/07 Agle of miimum deviatio - coditio of high symmetry - t i air icidet ray θ i θ t θ i δ mi θ t refracted ray prism B 9 Implicatios t i iv itt i v it t whe coditio for miimum deviatio i mi i AND t i sice t i vi t i t si si Sell ' s Law,st face solvig for mi si si si t si i Mai Result B, valid whe δ=δ mi Forms the basis of precise measuremets of the idex of refractio as a fuctio of. Measure δ mi () with a carefully costructed prism havig a precisely kow value of gives () with high precisio. 0 0

11 /0/07 Visible Lies i He Spectrum Bright Lies Dim Lies Color (m) Color (m) Red Red Yellow Gree Gree 50.6 Blue Gree 49. Violet 40.6 Blue 47.3 Blue-Violet 447. Measure δ mi for each wavelegth Calculate () Fit () to Cauchy s formula Estimate Abbe s umber for prism Cauchy Relatioship 836: Augusti-Louis Cauchy suggests simple empirical formula Typical Values Material C C (m ) Fused silica Borosilicate glass BK Hard crow glass K Barium crow glass BaK Barium flit glass BaF Dese flit glass SF Dese flit glass SF* C... C - Idex of refractio SF Glass Wavelegth (m) See * F. El Ghussei, J. M. Wrobel, ad M. B. Kruger, Am. J. Phys. 74, 888 (006).

12 /0/07 Calculus Review. Calculate small chage f i some fuctio f. Chai Rule: If some fuctio g depeds o some variable y ad y depeds o aother variable x, the g becomes a fuctio of x as well ad we ca write f(x) f df dx dg dx dg dy dy dx x x df f~ dx x 3 B. Resolvig Power ability to resolve two closely spaced wavelegths Assume coditio for miimum deviatio Icidet Light Two wavelegths: = -Δ & air prism δ δ mi s L L D δ L Refracted Light How does the deviatio agle δ chage with wavelegth? from calculus : d d from geometry : L L D D mi ta θ i B Defie resolvig power

/0/07 What is smallest measureable value of Δ? Smallest value for Δ is set whe ΔL assumes the smallest possible value that ca be resolved. This coditio is typically specified by settig ΔL smallest =.

13 /0/07 What is smallest measureable value of Δ? Smallest value for Δ is set whe ΔL assumes the smallest possible value that ca be resolved. This coditio is typically specified by settig ΔL smallest =. From geometry From calculus L D L smallest smallest D D d see Appedix mi smallest d dmi dmi d B d D D D d d d D d d B Mai Result C d Evaluate from Cauchy s Eq. Resolvig the Na doublet Na Doublet: m ad m gallery.et/gallery/displayimage.php?album=9&pos=34&pid=

14 /0/07 Material Schott Techical Desigatio Typical results - sample calculatio (for a prism with 4 cm base at =589 m) (m) d/d (i m) - dδ/d (i mrad/m) miimum Δ i m Crow glass BK E Flit glass SF E Up Next Diffractio Gratigs 8 4

15 /0/07 Appedix: Evaluatig dδ mi /d θ i π-(/+θi ) θ i D θ i s θ i prism B air s D θ t =θ i First, some geometry: D scos B B si s s si B B cosi D cosi si si D cosi B si Estimatig dδ mi /d mi si si i Result B si t si mi si si mi si si mi d d mi si si d si si d d si xsi A si i t i cosi dx x si A t si si d mi d si but at miimum deviatio t from Eq.( vi) si d mi d si si Sell ' s Law si si d mi d si A B D 30 5

/0/07 Appedix: Readig the agular Verier Scale 0 idex 0 0.

38 o Scales lie up, say here 0.5 o =30 0 This image is somewhat distorted. I the actual case, oly oe tick mark o the Verier scale should match up with oe lie o the Mai scale.

16 /0/07 Appedix: Readig the agular Verier Scale 0 idex =30 Read from the 0 idex o Verier scale Verier scale Mai scale 3 =60 0 Readig: betwee o ad o Upo ispectio: readig is betwee 0 ad 30 Verier scale tick mark readig: + 40 o Readig: o = o 40 =.38 o Scales lie up, say here 0.5 o =30 0 This image is somewhat distorted. I the actual case, oly oe tick mark o the Verier scale should match up with oe lie o the Mai scale. Most had-held calculators do ot uderstad agles i degrees ad miutes. Must covert! 3 Readig the agular Verier Scale (cotiued) Verier scale is i miutes: 0.5 o =30 Verier scale 30 Mai scale 0.5 o Read from the 0 idex o Verier scale Readig: betwee 53 o ad 54 o Upo ispectio: readig is greater tha 53 o 30 Verier scale tick mark readig: 8 Readig: 53 o =53 o 38 = o The image is somewhat distorted. I the actual case, oly oe tick mark o the Verier scale should match up with oe lie o the Mai scale. Most had-held calculators do ot uderstad agles i degrees ad miutes. Must covert to decimal otatio! 3 6

17 /0/07 M agular d d t i a si i si t d d cos d d d si i si t i i i cos t t cos cos t d d d Appedix: Agular magificatio of a prism t t i c d d d d t i i i t d d d d 0 i θ i Apex Iterface δ=δ +δ P δ δ θ t Q Base θ i R θ t Iterface air prism b si i si t d i t d si si d d cos d d i i d i i cos t d cos cos t i i t i i t d d 33 d d These idetities give M agular d d t t t i t cos i cos cos d d cos cos i cos cos cos t t cos cos t cos cos t i d d i Whe δ=δ mi t i i t M agular Whe t / (grazig emergece), cos( t ) 0 ad M agular 34 7

18 /0/07 Which diagram is correct? 35 8

PHYS 450 Fall semester Lecture 05: Dispersion and the Prism Spectrometer. Ron Reifenberger Birck Nanotechnology Center Purdue University

PHYS 450 Fall semester Lecture 05: Dispersion and the Prism Spectrometer. Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 450 Fall semester 06 Lecture 05: Dispersion and the Prism Spectrometer Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 05 Prisms Dispersion of Light n n As early as the 3th