Optics. Measuring the velocity of light Geometrical Optics. What you need:

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1 Geoetrical Optic Optic Meauring the velocity of light -01 What you can learn about Refractive index Wavelength Frequency Phae Modulation Electric field contant Magnetic field contant Principle: The intenity of the light i odulated with a high frequency and the phae rela tionhip of the tranitter and receiver ignal copared. The velocity of light i calculated fro the relationhip between the change in the phae, the odulation frequency and the light path. What you need: Speed of Light eter (coplete et) Screened cable, BNC, l = Digital Ocillocope 25 MHz, 2 channel Detektor Reflektor Laer Coplete Equipent Set, Manual on CD-ROM included Meauring the velocity of light P Principle of eaureent. Tak: 1. To deterine the velocity of light in air. 2. To deterine the velocity of light in water and to calculate the refractive index 3. To deterine the velocity of light in acrylic gla and to calculate the refractive index PHYWE Sytee GbH & Co. KG D Göttingen Laboratory Experient Phyic 89

2 Meauring the velocity of light LEP Related topic Refractive index, wavelength, frequency, phae, odulation, electric field contant, agnetic field contant. Principle The intenity of the light i odulated and the phae relationhip of the tranitter and receiver ignal copared. The velocity of light i calculated fro the relationhip between the change in the phae and the light path. Equipent Light velocity eauring app Screened cable, BNC, l = Ocillocope, 30 MHz, 2 channel Block, ynthetic rein Tak 1. To deterine the velocity of light in air. 2. To deterine the velocity of light in water and ynthetic rein and to calculate the refractive indice. Set-up and procedure The deviating irror and the lene are et up in uch a way that the incident and eergent light ray are parallel to the bae plate (Fig. 1) and a axiu ignal reache the receiving diode (detailed direction can be found in the operating intruction). The odulation frequency of 50.1 MHz (quartz tabilied) i reduced, to the approxiately 50 khz o that the tranitter and receiver ignal can be diplayed on the ocillocope. 1. Firt of all, the irror i placed a cloe to the operating unit a poible (zero point on the cale). A Liajou figure appear on the ocillocope (XY-operation) and i tranfored into a traight line uing the phae knob on the operating unit. The irror i then lid along the graduated cale until the phae ha changed by p, i.e. until a traight line loping in the oppoite direction i obtained. The irror diplaceent x i eaured; the eaureent hould be repeated everal tie. 2. The water-filled tube or the ynthetic rein block i placed in the path of the ray o that it end face are perpendicular to the optic axi; the irror i placed directly behind the (top of Fig. 3). A upporting block can be ued with the rein block o that the light pae through it in both direction. A traight line i obtained on the ocillocope again with the phae knob. The ediu i then taken out of the path of the Fig. 1: Experiental et-up for eauring the velocity of light in ynthetic rein. PHYWE erie of publication Laboratory Experient Phyic PHYWE SYSTEME GMBH & Co. KG D Göttingen P

3 LEP Meauring the velocity of light Fig. 2: Diagra of the experiental et-up for eauring the velocity of light in air. ray and the irror oved until the Liajou figure again how the ae phae difference. The irror diplaceent x i eaured everal tie. Theory and evaluation The velocity of light i obtained a follow fro Maxwell equation: c 1 (1) 2e 0 0 where e 0 = F i the electric field contant, 0 = i the agnetic field contant, e the relative perittivity of the ediu and it pereability. The refractive index of a ediu i the quotient of the light velocity in a vacuu and in the ediu. n 2e H = 1 for ot tranparent ubtance. Relative perittivity and refractive index are dependent of frequency (diperion) becaue of the natural vibration of ato and olecule. Red light (LED) i ued in the experient. The phae relationhip between tranitter and receiver ignal i repreented by a Liajou figure on the ocillocope. If it i a traight line, the phae difference i 0 in the cae of a poitive lope and p in the cae of a negative one. (2) 1. In order to eaure the velocity of light in air, the light path i extended by l = 2 x (Fig. 2), to produce a phae change of p: i.e. to travel thi ditance the light require a tie t = 1 2 f Fig. 3: Meauring the velocity of light in other edia. where f = 50.1 MHz, the odulation frequency. The velocity of light in air i thu expreed by c L l 4f x t (3) 2 P PHYWE erie of publication Laboratory Experient Phyic PHYWE SYSTEME GMBH & Co. KG D Göttingen

4 Meauring the velocity of light LEP The average of 10 eaureent wa: Value taken fro literature: 2. The velocity of light in water or ynthetic rein, c M, i eaured by coparing it with the velocity of light in air c L (Fig. 3). In the firt eaureent (with the ediu), the light travel a ditance l 1 in tie t 1. l 1 = 2x 1 t 1 1 1l c 1 l 2 1 l L c M In the econd eaureent (no ediu), the light travel a ditance in tie c L 12.98± c L l 2 = l x t 1 1 c L 1l 1 2 x2 The phae relationhip between tranitter and receiver ignal i the ae in both cae, o that In water, the ditance eaured l = 1, o that the ter k In ynthetic rein, for a ditance of 30 c, the ter k c L f l 6 k c L f l 20 k Fro the expected agnitude for the refractive index we can deduce that k = 0, therefore t 1 = t 2 (5) The eaureent in water give n H2 O = ± c H2 O = (2.23 ± 0.01) 10 8 Value fro literature: n H2 O = c H2 O = For the ynthetic rein block we obtain the following: t 1 t 2 k f ; k 0, 1, 2... n = ± ynthetic rein We thu obtain the refractive index n c L 2 x 1 k c L c M l f l (4) c = (1.87 ± 0.01) 10 8 ynthetic rein PHYWE erie of publication Laboratory Experient Phyic PHYWE SYSTEME GMBH & Co. KG D Göttingen P

5 LEP Meauring the velocity of light 4 P PHYWE erie of publication Laboratory Experient Phyic PHYWE SYSTEME GMBH & Co. KG D Göttingen