NAPREDNI FIZICKI PRAKTIKUM II

SMJER: PRVOSTUPNIK/MAGISTAR GEOFIZIKE

Prvi dio: FOTOELEKTRICNI EFEKT

PRVOSTUPNIK/MAGISTAR GEOFIZIKE NFP II 1

ZADATAK

Odredite Planckovu konstanu h iz mjerenja ovisnosti fotoelektricnog napona o

frekvenciji svjetlosti iz spektralne cijevi.

Dodatne upute za rad

Na elektricnom pojacalu postaviti prekidac nacina rada u polozaj “Electrometer”

(veliki ulazni otpor), vremensku konstantu (time constant) u polozaj 0.1 ili 0.3,

a pojacanje (amplification) u polozaj 100. Prije svakog mjerenja valja anodu

fotocelije zagrijati (najvise do 10 sec) s ciljem uklanjanja parazitskih napona.

Toplinska ravnoteza fotocelije uspostavi se ponovno priblizno nakon 30 sec, te

se tada moze izvesti mjerenje. Izbijanje naboja se vrsi gumbom Discharge na

pojacalu.

LEP5.1.04

-00

Planck’s “quantum of action” from photoelectric effect(line separation by interference filters)

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen 25104-00 1

Related topicsExternal photoelectric effect, work function, absorption, pho-ton energy, anode, cathode.

PrincipleA potassium photo-cell is illuminated with light of differentwavelengths. Planck’s quantum of action, or Planck’s con-stant (h), is determined from the photoelectric voltages meas-ured.

EquipmentPhotocell, for h-det., w. housing 06778.00 1Interference filters, set of 3 08461.00 1Interference filters, set of 2 08463.00 1Experiment lamp 6 11615.05 1Spectral lamp Hg 100, pico 9 base 08120.14 1Power supply for spectral lamps 13662.97 1Mounting plate R, 16 cm�21 cm 13002.00 1Universal measuring amplifier 13626.93 1Digital multimeter 07134.00 1Screened cable, BNC, l = 300 mm 07542.10 1Connecting cord, l = 250 mm, red 07360.01 1Connecting cord, l = 250 mm, blue 07360.04 1

TasksTo determine Planck’s quantum of action from the photoelec-tric voltages measured at different wavelengths.

Set-up and procedureThe experimental set-up is as shown in Fig. 1. The interfer-ence filters are fitted one after the other to the light entranceof the photo-cell.

The measuring amplifier is used in the following way

– Electrometer Re ≥ 10137

– Amplification: 100

– Time constant: 0

– Voltmeter: DC 2V

The high-impendance input of the measuring amplifier isdischarged via the ‘zero’ button between measurements.

Theory and evaluationHalf of the inside of the high-vacuum photo-cell is a metal-coated cathode. The anular anode is opposite the cathode.

Fig. 1: Experimental set-up for determining Planck’s quantum of action.

LEP5.1.04

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Planck’s “quantum of action” from photoelectric effect(line separation by interference filters)

25104-00 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen2

If a photon of frequency f strikes the cathode, then an elec-tron can be ejected from the metal (external photoelectriceffect) if there is sufficient energy.

Some of the electrons thus ejected reach the (unilluminated)anode so that a voltage is set up between anode and catho-de, which reaches the limiting value U after a short (charging)time. The electrons can only run counter to the electric fieldset up by the voltage U if they have the maximum kinetic ener-gy, determined by the light frequency,

(Einstein equation),

where A = work function from the cathode surface, v = elec-tron velocity, m = rest mass of the electron.

Electrons will thus only reach the anode as long as their ener-gy in the electric field is equal to the kinetic energy:

with e = electron charge = 1.602 · 10-19 As

An additional contact potential f occurs because the surfacesof the anode and cathode are different:

If we assume that A and f are independent of the frequency,then a linear relationship exists between the voltage U (to bemeasured at high impedance) and the light frequency f:

If we assume U = a + bf to the values measured in Fig. 2 weobtain:

h = (6.7 ± 0.3) · 10-34 Js

Literature value: h = 6.62 · 10-34 Js.

U � �1A � f 2

e�

h

e f

eU � f �m

2 v2

eU �m

2 v2

hf � A �m

2 v2

Fig. 2: Voltage of the photo-cell as a function of the frequencyof the irradiated light.

NAPREDNI FIZICKI PRAKTIKUM II

SMJER: PRVOSTUPNIK/MAGISTAR GEOFIZIKE

Drugi dio: POLARIZACIJA

SVJETLOSTI

PRVOSTUPNIK/MAGISTAR GEOFIZIKE NFP II 1

ZADACI

1. Izmjerite ovisnost intenziteta linearno polarizirane svjetlosti o kutu jednog

analizatora. Na temelju mjerenja napisite sto mozete zakljuciti o laserskom

izvoru svjetlosti na vjezbi.

2. Izmjerite ovisnost intenziteta svjetlosti o medusobnom kutu dvaju polari-

zatora, za razne kuteve prvog polarizatora. Posebnu paznju obratite na

slucaj kada je prvi polarizator zakrenut za 45◦, a drugi za 90

◦ u odnosu

na ravninu polarizacije izvora svjetla. Sto se dogada kada prvi polarizator

maknemo? Objasnite rezultat.

LEP2.5.01

-00Polarisation by quarterwave plates

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen 22501-00 1

Related topicsPlane, circularly and elliptically polarised light, polariser, analyser,plane of polarisation, double refraction, optic axis, ordinary andextraordinary ray.

PrincipleMonochromatic light falls on a mica plate perpendicular to itsoptic axis. At the appropriate plate thickness (M/4, or quarter-wave plate) there is a 90° phase shift between the ordinary andthe extraordinary ray when the light emerges from the crystal.The polarisation of the emergent light is investigated at differ-ent angles between the optic axis of the M/4 plate and thedirection of polarisation of the incident light.

EquipmentPhotoelement f. opt. base plt. 08734.00 1Lens holder 08012.00 3Lens, mounted, f = +100 mm 08021.01 1Diaphragm holder 08040.00 2Iris diaphragm 08045.00 1Double condenser, f = 60 mm 08137.00 1Lamp, f. 50 W Hg high press. lamp 08144.00 1Power supply for Hg CS/50 W lamp 13661.97 1Interference filter, yellow, 578 nm 08461.01 1Polarising filter, on stem 08610.00 2Optical profile-bench, l = 1000 mm 08282.00 1Base f. opt. profile-bench, adjust. 08284.00 2Slide mount f. opt. pr.-bench, h = 30 mm 08286.01 8Slide mount f. opt. pr.-bench, h = 80 mm 08286.02 1Polarization specimen, mica 08664.00 2Digital multimeter 07122.00 1Universal measuring amplifier 13626.93 1Condenser holder 08015.00 1Connecting cord, l = 750 mm, red 07362.01 1Connecting cord, l = 750 mm, blue 07362.04 1

Tasks1. To measure the intensity of plane-polarised light as a func-

tion of the position of the analyser.

2. To measure the light intensity behind the analyser as a func-tion of the angle between the optic axis of the M/4 plate andthat of the analyser.

3. To perform experiment 2. with two M/4 plates one behindthe other.

Set-up and procedureThe experiment is set up as shown in Fig. 1. The experimentlamp with the double condenser (focal length 60 mm) fitted,the lens holder with the iris diaphragm, the lens holder with theinterference filter, the polariser, the holder with the M/4 plate,the lens holder with the lens of focal length 100 mm, the anal-yser, and the distributor support with the silicon photo-cell areall set up on the optical bench.

First of all the path of the ray is adjusted so that the photo-cellis well illuminated (this is done without the M/4 plate). With thepolariser on zero, the analyser is then rotated until the lightwhich it transmitted is of minimum intensity. The M/4 plate isnow clamped in the holder and rotated so that the light pass-ing through the analyser is again at minimum intensity. Theplane of polarisation of the light emerging from the polarisernow makes an angle of 0° (or 90°) with the optic axis of theM/4 plate. The light intensity is measured as a function of theposition of the analyser, for angles of 0, 30, 45, 60 and 90°,over the range –90° to +90°. The resistor is plugged in par-allel to the entry of the measuring amplifier.

The current intensity of the photo-cell is proportional to theintensity of the incident light.

Fig. 1: Experimental set-up for determining the type of polarisation of the emergent light.

LEP2.5.01

-00Polarisation by quarterwave plates

22501-00 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen2

Fig. 2: Splitting of polarised light in a double-refracting crystal(P = polariser, A = analyser).

Theory and evaluationThe velocity of the light travelling in the direction of the opticaxis of a double-refracting crystal has the same value, co,whatever the direction of its plane of polarisation. When trav-elling at right angles to the optic axis, polarised light has thesame velocity co, when the electric vector is perpendicular tothe optic axis (ordinary ray, see Fig. 2). If the electric vector isparallel to the optic axis the light velocity c p co (extraordinaryray).

E0 is the amplitude of an electric field vector emerging from thepolariser and G the angle between the direction of polarisationP and the optic axis of a double-refracting crystal.

From Fig. 2 we derive the following for the amplitudes of theordinary and of the extraordinary ray:

E1 (t) = E0 (t) · sin G(1)

E2 (t) = E0 (t) · cos G

At time t, the state of vibration in the two rays at the crystalsurface is described by:

E1 (t) = E0 (t) · sin G · sin Wt(2)

E2 (t) = E0 (t) · cos G · sin Wt

In the case of double-refracting crystals (M/4 plates), the thick-ness

(3)

where no is the refractive index of the ordinary ray and nao thatof the extraordinary ray in the crystal, causes a path differenceof M/4 (i.e. a phase difference of Q/2) between the two rays

when they combine to a resultant ray on emerging from thecrystal. From (2) we obtain

Ex = E1 = E0 · sin G · sin Wt(4)

Ey = E2 = E0 · cos G · cos Wt

(4) is the parametric representation of an E vector rotating inthe direction of propagation, i.e. perpendicular to the x and yaxis, about a fixed axis.

For angles of G = 0° and G = 90° we obtain plane polarisedlight of intensity

(5)

For an angle of 45°, sin G = cos G = , and the amount ofthe rotating E vector is

(6)

The light is circularly polarised and of intensity

I = � (7)

and is transmitted without loss of intensity in all analyser posi-tions.

Fig. 3: Intensity distribution of plane-polarised light as a func-tion of the position of the analyser (without M/4 plate).

E02

2I0

2

E � 2Ex2 � Ey

2 �E022

122

I � I0 � E02 .

dl4 �M

4 ·

1no – nao

,

Polarisation by quarterwave platesLEP

2.5.01-00

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen 22501-00 3

Fig. 4: Intensity distribution of polarised light as a function ofthe direction of transmission of the analyser: with M/4plate at various angular settings.

At all angles G other than 0°, 45° and 90°, the transmittedlight is elliptically polarised. The tip of the E vector rotatingabout the axis parallel to the direction of propagationdescribes an ellipse with the semi-axes.

Ea = E0 sin G (x-direction)(8)

Eb = E0 cos G (y-direction)

For the intensity of the light transmitted by the analyser in therespective directions, we have:

(9)

By rotating the analyser we obtain the following for the ratio ofthe maximum to the minimum transmitted light intensity:

(10)

For any angular setting X between the analyser and the opticaxis of the M/4 plate, we have:

(11)

Fig. 5: Intensity distribution of polarised light: with M/2 plate atvarious angular settings.

First of all the intensity distribution of plane-polarised light ismeasured as a function of the analyser position, without theM/4 plate in the path of the rays (Fig. 3).

The type of polarisation of the transmitted light is determinedfrom the corresponding intensity distribution values, for vari-ous angles between the optic axis of the M/4 plate and thedirection of transmission of the analyser (Fig. 4).

If two M/4 plates are set one behind the other, plane-polarisedlight is produced whatever the direction of the optic axis of theM/2 plate so created (Fig. 5).

I � E02 · cos2 f · cos2 w � E0

2 · sin2 f · sin2 w

Ia

Ib�

Ea2

Eb2 �

sin2f

cos2f� tan2 f

Ib � Eb2 � E0

2 cos2 f

Ia � Ea2 � E0

2 sin2 f

LEP2.5.01

-00Polarisation by quarterwave plates

22501-00 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen4