Bestimmung der Dichte eines=20 Newtonspiegels

Um die Dichte ausrechnen zu k=C3=B6nnen, = brauchen Sie den=20 Durchmesser vom Spiegeltr=C3=A4ger (d. h. einfach den = =C3=A4u=C3=9Feren Durchmesser der=20 Scheibe, NICHT den etwas kleineren Durchmesser der verspiegelten = Fl=C3=A4che),=20 die Dicke vom Spiegel (am Rand gemessen), das Gewicht sowie die=20 Brennweite.

Wer sich nicht mit dem Formelkram plagen will, = benutzt=20 einfach unseren Dichte-Rechner.

Zur Genauigkeit: Diese Messung benutzen Sie = prim=C3=A4r um=20 herauszufinden, ob ein Spiegel aus Pyrex ist oder nicht. Da die = Dichte von=20 Pyrex um rund 12% unter der aller anderen g=C3=A4ngigen = Materialien liegt,=20 braucht man die Werte nicht allzu genau. Erst wenn Sie bei allen = drei=20 gemessenen Werten einen unrealistisch gro=C3=9Fen Fehler von 4% = haben, wird das=20 Ergebnis im schlimmsten Fall auf 12% ungenau.

Wenn man nur ein Lineal zur Verf=C3=BCgung = hat, wird man=20 naturgem=C3=A4=C3=9F den gr=C3=B6=C3=9Ften Fehler bei der Messung = der Dicke machen. Auf einen=20 halben millimeter genau sollte kein Problem sein; das ist dann bei = einer=20 Dicke von 25mm ein Fehler von 2%. Mit einer Schieblehre kann man = zehnmal=20 genauer messen. Ein Fehler beim Durchmesser von einem mm = entspricht 0,5%=20 bei einem 8" Spiegel. Die Waage sollte einigerma=C3=9Fen = verl=C3=A4=C3=9Flich sein. Bei=20 einer elektronischen Briefwaage kann man von einem Fehler unter 1% = ausgehen. Damit sind die Fehler alle zusammen auch im schlimmsten = Fall=20 (wenn sich die Fehler alle in der gleichen Richtung addieren) = dreimal=20 kleiner als die hier notwendige Genauigkeit. Auch eine = K=C3=BCchenwaage ist f=C3=BCr=20 unseren Zweck ausreichend genau. F=C3=BCr gr=C3=B6=C3=9Fere = Spiegel braucht man eine=20 Versandwaage oder etwas Vergleichbares.

Zur Berechnung:

Der Spiegeltr=C3=A4ger wird zun=C3=A4chst als = Zylinder mit dem=20 gemessenen Durchmesser D und der gemessenen Dicke = d=20 betrachtet. Das Volumen des Zylinders ist:

3D""=20

Um das Volumen des Spiegels zu berechnen, = mu=C3=9F noch das=20 ausgeschliffene Volumen abgezogen werden (bei einem 8" f/6 etwa 30 = Kubikzentimeter). Da bei Newton-Spiegeln die Abweichung des = Paraboloids=20 von der Kugelform nur wenige Mikrometer betr=C3=A4gt, kann in sehr = guter=20 N=C3=A4herung das Volumen eines Kugelabschnittes genommen werden: =

3D""=20

r:	ist der Radius der Kugel (=3D doppelte=20 Brennweite)
h:	ist die Tiefe des ausgeschliffenen=20 Kugelabschnittes oder der sogenannte Sagitta = s
f:	ist die Brennweite des=20 Spiegels

3D""=20

Mit dem errechneten Volumen und dem Gewicht = (eigentlich=20 Masse m) ergibt sich die Dichte zu:

3D""=20

Die Fase (schr=C3=A4ge Kante am Spiegelrand) = kann bei der=20 hier n=C3=B6tigen Genauigkeit vernachl=C3=A4ssigt werden, genauso = wie das Gewicht=20 der Beschichtung, da diese h=C3=B6chstens einige hundert nanometer = dick ist.=20

ICS und Intercon Spacetec sind eingetragene = Warenzeichen der=20 Intercon GmbH Augsburg. =C2=A9 Copyright: 1994-2008 Martin Birkmaier - = Intercon GmbH,=20 Augsburg
Intercon GmbH, Gablinger Weg 9k, D-86154 Augsburg. E-Mail = info (at)=20 intercon-spacetec.de, Fax: 0821-414085 Tel.: 0821-414081

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){9.13()}9.P(F-1)}}y{4((16=3D=3D"n")||(12=3D=3D39)){4(F!=3D(J.L-1)){9.24(= );4(K){9.13()}9.P(F+1)}}y{4((16=3D=3D"s")||(12=3D=3D4R)){4(K){9.13()}y{9.= 2i()}}}}}},2L:7(){4((J.L-1)>F){3F=3DG = 1U();3F.1H=3DJ[F+1][0]}4(F>0){3g=3DG = 1U();3g.1H=3DJ[F-1][0]}},17:7(){B.24();$("1p").N();G = 19.4O("1G",{18:23});3E();3D();4(K){U(5 = i=3D0;i<1A;i++){C.2D(1B[i])}K=3Dz}}};7 31(){5 = a,Y;4(1g.3C){Y=3D1g.3C;a=3D1g.4K}y{4(6.11&&6.11.2v){Y=3D6.11.2v;a=3D6.11.= 3B}y{4(6.R){Y=3D6.R.2v;a=3D6.R.3B}}}3z=3DG 1d(a,Y);E 3z}7 2c(){5 = a,Y;4(C.22&&C.3o){a=3DC.3q+C.4H;Y=3DC.22+C.3o}y{4(6.R.3w>6.R.3v){a=3D6.R.= 4G;Y=3D6.R.3w}y{a=3D6.R.32;Y=3D6.R.3v}}5 = b,1f;4(1g.22){4(6.11.20){b=3D6.11.20}y{b=3D1g.3q}1f=3D1g.22}y{4(6.11&&6.1= 1.2s){b=3D6.11.20;1f=3D6.11.2s}y{4(6.R){b=3D6.R.20;1f=3D6.R.2s}}}4(Y<1f){= 2r=3D1f}y{2r=3DY}4(a=3D 4);=0A= if ((browserName =3D=3D "Netscape" && browserVer >=3D 3) || msie4 || = browserName=3D=3D"Konqueror" || browserName=3D=3D"Opera") {version =3D = "n3";} else {version =3D "n2";}=0A= // Blurring links:=0A= function blurLink(theObject) { //=0A= if (msie4) {theObject.blur();}=0A= }=0A= ------=_NextPart_000_0000_01C8C41C.DD7945E0--