Experiments with light-emitting diodes
Yaakov Kraftmakhera)
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
(Received 15 February 2011; accepted 16 May 2011)
The radiant and luminous power spectra, efficiency, and luminous efficacy of commercially
available light-emitting diodes (LEDs) are measured. The output radiant power is determined with
a silicon photodiode from its typical spectral response. A calculation of the radiant power spectra
and the luminous power spectra is demonstrated. The frequency response of the LEDs is
determined in the range 10–107 Hz. For the white LED, the frequency response of the primary blue
emission and the green-yellow phosphorescence is measured separately, and the phosphorescence
time constant is estimated. The ratio h/e is estimated using the emission wavelengths and the “turnon” voltages. VC 2011 American Association of Physics Teachers.
[DOI: 10.1119/1.3599072]
I. INTRODUCTION
II. THE SETUP
A light-emitting diode (LED) is a semiconductor device
with a p-n junction that emits photons when electric current passes through it.1–3 The semiconductor crystal is
doped to fabricate an n-type region and a p-type region,
one above the other. Forward electrical bias across the
LED causes the holes and electrons to be injected from
opposite sides of the p-n junction into the active area,
where their recombination results in emission of photons.
The energy of the emitted photons is approximately the
band-gap energy of the semiconductor. The band-gap
energy of ternary and quaternary semiconductor compounds can be adjusted in a certain range by varying their
composition.
The first LEDs were homojunction diodes in which the
material of the core layer and that of the surrounding clad
layers are identical. Then heterostructures with layers having
a varying band-gap and refractive index were recognized as
advantageous. Contemporary LEDs are more complicated
double heterostructure diodes.
LEDs are efficient light sources for many applications,
including indicators, large-area displays, and opto-couplers.
Holonyak4 pointed out that the LED is an ultimate light
source. Mayer5 has considered the current status and prospective of solid-state lighting, where the LED is an excellent alternative to incandescent and fluorescent light bulbs.
LEDs are easily modulated sources and are widely used in
optical communications with optical fibers.6 The possibility
to modulate LEDs in a broad frequency band is crucial for
simultaneously transmitting many television or audio programs through a single optical fiber. To correctly reproduce
the programs, the amplitude modulation characteristic should
be linear.
LEDs can be used to demonstrate their basic properties7–15
and as auxiliary tools for many experiments and demonstrations.16–19 The experiments described in the following can be
considered as an addition to those published earlier.7–15 Important topics are the determination of the output radiant
power, the radiant and luminous power spectra, and the luminous efficacy of LEDs. For a white LED, the frequency
response of the primary blue emission and of the green-yellow
phosphorescence is measured separately. The value of h/e is
calculated from the emission wavelengths and the “turn-on”
voltages.
Three color LEDs and one white LED from HuiYuan OptoElectronic20 were used in the experiments: LB-P200R1C-H3
(red), LB-P200Y1C-H3 (yellow), LB-P200B2C-H3 (blue),
and LB-P20WC3-60 (white). The input current of the LEDs
indicated by the supplier is 0.75 A. In the experiments we will
discuss, the maximum input current is 0.1 A, and the input
power does not exceed 0.3 W.
Two types of white LEDs are available. One type combines two or three LEDs of appropriate colors. With such a
device, a spectrum similar to that of daylight is achievable.
Modifications of the light from “warm white” to “cool
daylight” are possible by varying the contributions of the
components. In the other type a suitable phosphor is positioned onto a blue LED, so that the output light contains blue
light and a Stokes-shifted phosphorescence band. The white
LED we used is of the second type.
An important characteristic of a lighting source is the
color temperature (see, for example, Ref. 21). The color temperature does not mean that the spectrum of a light source is
similar to that of a blackbody of equal temperature. Fluorescent lamps and LEDs are designed to emit only visible light.
Therefore, their spectra differ radically from those of thermal
sources governed by Planck’s distribution, which unavoidably include intensive infrared emission. The spectrum of a
lighting source can be characterized by the blue-to-red ratio,
which can be made to be equal to that of a blackbody at a
given temperature. This ratio determines the color temperature of the source. The green band in the spectrum is needed
for attaining high luminous efficacy of lighting sources (see
the following). For the white LED we used, the supplier
claims that the color temperature is in the range 6000–7000
K. This value is typical for “cool daylight” lamps. For “warm
white” lamps, the color temperature is in the range 2700–
3300 K.
The input electric current and power, radiant output
power, and efficiency of the LEDs can be measured or calculated, and then displayed versus the voltage applied to the
device or versus the current passing through it. With a dataacquisition system, the measurements are possible in a short
time. We use the ScienceWorkshop data-acquisition system
with DataStudio software from PASCO.22 The LED of interest is connected in series with a 10 X limiting resistor to the
Signal generator in the ScienceWorkshop 750 Interface. The
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http://aapt.org/ajp
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Fig. 1. General scheme of the experiments: (a) output radiant power and efficiency; (b) emission spectra; and (c) frequency response. PD represents
photodiode.
Output voltage is the Positive ramp up voltage linearly
increasing from zero to a maximum value set to achieve the
maximum desired current through the LED. The period of
the Output voltage is 20 s. The Signal generator operates in
Auto mode: it starts to generate the Output voltage after starting a run. The option Automatic stop is used for automatically ending each run.
The output radiant power of the LEDs is determined with
a silicon photodiode by using its typical spectral response.
The radiant power spectra are obtained with a diffraction
grating and converted to the luminous power spectra by
using the standard luminosity function. The frequency
response of a LED is determined by sine-wave modulation
of the feeding current. Setups used in the experiments are
schematically shown in Fig. 1.
III. MEASUREMENTS AND RESULTS
A. Radiant Power and Efficiency
The input current i of the LEDs is measured directly as the
Output current of the Signal generator. DataStudio calculates the voltage applied to the LED as the Output voltage
minus the Output current times the resistance of the limiting
resistor, 10 X. The input electric power is calculated from
the input current and applied voltage. Immediately after a
run, DataStudio displays the input current and power versus
the applied voltage (see Fig. 2).
To determine the output radiant power of an LED, its light
is directed onto a silicon photodiode (United Detector Technology, PIN-10D) positioned adjacent to the LED. The sensitive area of the photodiode is about 1 cm in diameter, so that
the light from the LED is almost fully utilized. The Voltage
sensor acquires the voltage on a 100 X load resistor of the
photodiode.
The output radiant power (radiant flux) of an LED is calculated from the photoelectric current and the spectral
response of the photodiode R(k), that is, the wavelength dependence of the ratio of the photodiode current I to the incident radiant power P. Usually, the function R(k) is given by
manufacturers as a graph. In the range 400–800 nm, the
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Fig. 2. (Color online) Input current and power consumed by the LEDs versus the applied voltage. Red (R), yellow (Y), blue (B), and white (W). The
turn-on voltage increases with the energy of the emitted photons.
spectral response of the photodiode taken from such a graph
can be represented as
RðkÞ ¼ I=PðA=WÞ ¼ 1:2 103 ðk300Þ;
(1)
where k is the wavelength in nanometers. With minor modifications, Eq. (1) holds for all silicon photodiodes. This
approach is not as precise as a measurement with a sensor
based on the thermal action of absorbed light. However, it is
much simpler and satisfactory for our purposes.
DataStudio displays the output characteristics of an LED
versus the input current (Fig. 3). The output radiant power is
nearly proportional to the input current, and thus the rapid
increase of the input current or power indicates the threshold
of the LED emission.
For the color LEDs, the wavelengths for Eq. (1) are taken
to be at the peaks of the radiant power spectra (see the following). For the white LED, the mean wavelength is taken
as 550 nm. This simplification introduces an additional
uncertainty to our results. For 100 mA input currents, the
output radiant power of the LEDs ranges from 13 mW (yellow) to 53 mW (white). The efficiency is the ratio of the output radiant power to the input electric power. For the LEDs
tested, the efficiency ranges from 0.065 (yellow) to 0.19
(white). For input currents in the range of 10–40 mA, the efficiency of the white LED is even higher and is 0.21.
In an ideal LED every electron-hole recombination produces one output photon of energy nearly equal to the bandgap energy. The external quantum efficiency of such an LED
thus equals unity. Similarly, an ideal photodiode produces
one electron for every incident photon, and hence its external
quantum efficiency also equals unity (see Ref. 4). For the
combination of an ideal LED and an ideal photodiode, the ratio of the current produced by the photodiode to the input
current of the LED thus should be one. For real devices, this
current ratio shows how close the LED is to this ultimate
limit. The external quantum efficiency of LEDs is much
lower than their internal efficiency because of the difficulty
of extracting light from the device. The current ratio for the
Yaakov Kraftmakher
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Fig. 4. (Color online) (a) Measured radiant power spectra of the LEDs and
(b) normalized spectra. The measured spectra are normalized to make the integral of every spectrum equal to the total radiant power determined with the
silicon photodiode.
Fig. 3. (Color online) Output characteristics of the LEDs versus input current: (a) output radiant power, (b) efficiency, and (c) current ratio, a measure
of the quantum efficiency of the LED–photodiode combination. The output
radiant power is nearly proportional to the input current.
LEDs that we tested ranges from 0.045 (yellow) to 0.16
(white). Because the external quantum efficiency of a silicon
photodiode is sufficiently high (see, for example, Ref. 23),
the low values of the current ratio are caused mainly by the
low external quantum efficiency of the LEDs.
It is easy to find a relation between the external quantum
efficiency of a LED, g1, and of a photodiode, g2, and the current ratio of the LED–photodiode combination. We assume
that the energy of photons emitted by the LED, h, equals
the bang-gap energy, eVg (e is the electron charge), and that
the emission occurs when the voltage applied to the LED is
Vg, and the current is i. The power consumed by the LED is
iVg, and the output radiant power is P ¼ g1nh ¼ g1iVg,
where n ¼ i/e is the number of electrons passing through the
LED per unit of time. The external quantum efficiency of the
LED thus equals its electrical efficiency. The external quantum efficiency of a photodiode is the ratio of the number of
electrons N2 ¼ I/e produced per unit of time to the number of
incident photons N1 ¼ P/h ¼ P/eVg. Therefore, g2 ¼ N2/N1
¼ (I/P)Vg ¼ R(k)Vg. The current ratio I/i of the LED–photodiode combination thus equals g1g2.
B. Radiant Power Spectra
The emission spectra of the LEDs are determined with the
PASCO Educational spectrophotometer (OS-8537), two
lenses, and a diffraction grating with 600 lines per millimeter. The PASCO Light sensor (CI-6504A) and the Aperture bracket (OS-8534A) are also used. Initially, the sensor
is set at the zero diffraction angle. With the Delayed start
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and Automatic stop options, the measurement data are
acquired in the wavelength range from 350 to 750 nm. The
spectra may be distorted because the efficiency of diffraction
gratings depends on wavelength, and for the grating we used,
this dependence is unknown.
The emission spectra corrected by the use of Eq. (1) are
radiant power spectra (in arbitrary units). The spectra of the
color LEDs have one peak near the center of the emission
band: 465 nm (blue), 585 nm (yellow), or 625 nm (red). The
full width of the spectra at half a maximum is nearly 30 nm
(see Fig. 4).
The radiant power spectrum of the white LED has a peak
in the blue band and a wide green-yellow phosphorescence
band with a maximum at 555 nm. To make the phosphorescence evident, it is sufficient to illuminate the LED by blue
light from outside. With the blue LED we used, the greenyellow phosphorescence is clearly seen. This observation
confirms that the LEDs can be used for observing phosphorescence spectra. For instance, when we focus the light from
the blue LED on the screen of a cathode-ray tube, the spectrum of the phosphorescence is observable by looking at the
screen through a diffraction grating. The spectrum can be
compared with the cathodoluminescence spectrum of the
screen (see, for example, Ref. 24).
To calculate the true radiant power spectra of the LEDs,
the radiant power spectrum of each LED (in arbitrary units)
is integrated over all wavelengths with Origin software.25
Then each spectrum is normalized to make the integral equal
to the output radiant power determined with the silicon photodiode. This operation provides the true radiant power spectra, that is, the wavelength dependency of the radiant power
per unit wavelength, Pk(k) (mW/nm). The next step is the
conversion of the radiant power spectra to luminous power
spectra.
Yaakov Kraftmakher
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C. Luminous Power Spectra
The radiant power spectrum is an insufficient characteristic of a lighting source because the human eye is not equally
sensitive to the light of different colors. The typical human
eye spectral response is given by the standard luminosity
function S(k) established by the International Commission
on Illumination. For light-adapted vision, this function has
a maximum at 555 nm and can be approximated by a
simple equation proposed by Agrawal et al.26
SðkÞ ¼ expð88x2 þ41x3 Þ;
(2)
where x ¼ k/555 – 1, and k is the wavelength in nanometers.
For our purpose, this approximation is satisfactory. However,
one should use the original numerical data for precise
calculations.
The spectral response of the human eye is a crucial factor
for providing effective and qualitative (similar to daylight)
lighting. The two requirements are in obvious contradiction:
qualitative lighting assumes the presence of blue and red
bands, which is ineffective because of the nature of human
vision. Initially, the base unit of luminous intensity, the candela (cd), was based on a “standard candle.” The present-day
definition of this unit adopted in 1979 says: “The candela is
the luminous intensity, in a given direction, of a source that
emits monochromatic radiation of frequency 540 1012 Hz
and that has a radiant intensity in that direction of 1/683 watt
per steradian.”27 The frequency 540 1012 Hz corresponds
to k ¼ 555 nm, while the factor 1/683 was chosen to match
the original definition of the candela. The lumen (lm) is
defined as 1 lm ¼ 1 cd sr. A light source of one candela provides a total luminous power (luminous flux) of 4p % 12.57
lm. By definition, one watt of electromagnetic radiation at
k ¼ 555 nm produces a luminous power of 683 lm.
The ratio of the total luminous power from a light source
to the electric power consumed is called the luminous efficacy. The maximum possible luminous efficacy of a light
source thus equals 683 lm/W, while much lower values
should be expected when the emission includes blue and red
optical bands.
The luminous power spectrum, that is, the wavelength dependence of the luminous power per unit wavelength, Fk(k)
(lm/nm), is obtained by multiplying the radiant power spectrum by 683 (lm/W) and then by the standard luminosity
function S(k). This conversion significantly changes the
spectra (see Fig. 5). The luminous power spectrum of
the white LED has only one maximum at 555 nm; however,
the blue emission is evidently pronounced.
D. LEDs as Lighting Sources
The total luminous power F from a light source is obtained
by integrating its luminous power spectrum,
ð1
FðlmÞ ¼
Fk ðkÞdk:
(3)
0
In our case, the integration is performed with Origin software. Among the LEDs tested, the white LED produces the
maximum luminous power of nearly 15 lm.
The luminous efficacy of the LEDs appears to be 33 (red),
33 (yellow), 12 (blue), and 55 lm/W(white). The supplier
gives values of the applied voltage and the total luminous
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Fig. 5. (Color online) (a) Standard luminosity function S(k) and (b) luminous power spectra of the LEDs. The latter are equal to the radiant power
spectra times S(k) and 683 (lm/W).
power of the LEDs and their tolerances. With mean values
of the supplier’s data, the efficacy should be 32 (red), 34
(yellow), 11 (blue), and 67 lm/W (white). The agreement
between the two sets of data confirms that our experiments
are free of significant errors. Note that the luminous efficacy
is in the range 10–20 lm/W for incandescent lamps and 30–
110 lm/W for fluorescent lamps.5
E. The Frequency Response
The frequency response of LEDs is very important for optical communication. Infrared light is commonly used with
optical fibers due to its less attenuation and dispersion. The
signal encoding is typically simple intensity modulation. For
teaching purposes, modulated LEDs have been employed in
a simple telemetric system28 and for transmitting video signals through a light guide.29
The setup for measuring the frequency response of the
LEDs is similar to that used earlier.29 A dc supply and a
function generator, Hewlett-Packard 33120A, each with an
additional 100 X resistor at the output, are connected in parallel to the LED, and the limiting 10 X resistor is excluded.
The output voltage of the dc supply is set to obtain a 100 mA
current through the LED. With two lenses, the light from the
LED is focused on the sensitive area of a fast photodiode
(United Detector Technology, PIN-5D) operated with a 9 V
battery. The signal on a 150 X load resistor of the photodiode
is observed with an oscilloscope, Kenwood CS-4025. The ac
voltage applied to the LED is sufficiently small, and therefore the ac signal from the photodiode is nearly sinusoidal.
The frequency response was determined in the range of 10–
107 Hz. The characteristics are similar for all the LEDs
tested. The frequency response is constant up to 103 Hz and
slightly decreases up to 106 Hz, and then rapidly falls.
Because the LEDs have an internal resistance, capacitance,
and even inductance,30 the actual voltage across the p-n junction is unknown, and becomes frequency dependent at high
Yaakov Kraftmakher
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Table I. Parameters of the LEDs for 100 mA input currents. The frequency
f0.5 corresponds to 50% response. The value of h/e ¼ VFk/c.
Fig. 6. (Color online) (a) Frequency response of the white LED: ( ) primary blue band, ( ) green-yellow phosphorescence band. (b) With an
enlarged scale, the lag of the phosphorescence at high frequencies is clearly
seen.
frequencies. The frequency response presented here relates
to the ac voltage at the output of the function generator.
By measuring the frequency response it is possible to distinguish the primary blue emission and the green-yellow
phosphorescence of the white LED. The two optical bands
were separated with color filters, and the frequency response
for each band was determined independently. The time constant of the phosphor is very short, and thus the phosphorescence well follows the primary light modulation up to about
106 Hz. From the data obtained, only a rough estimation of
the time constant of the phosphor is possible and was found
to be of the order of 10–8 s (see Fig. 6).
For frequencies up to 106 Hz, all the LEDs tested provide
nearly 100% light modulation. Therefore, they can be
employed for determining the time constant of phosphors,
for which their radiation is sufficient to activate the
phosphorescence.
F. Determination of h/e
Optical emission from LEDs appears when the applied
voltage reaches a definite value VF, the forward “turn-on”
voltage. This threshold is assumed to be close to Vg. The
energy of emitted photons is hc/k, where c is the speed of
light, and h is Planck’s constant. By taking this energy equal
to eVF or eVg, it is possible to determine h/e by a simple
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LED
Red
Yellow
Blue
White
k (nm)
VF (V)
Input power (mW)
Output radiant power (mW)
Efficiency
Luminous power (lm)
Luminous efficacy (lm/W)
f0.5 (MHz)
h/e (10–15 J s/C)
625
1.8
185
32
0.17
6.15
33
585
1.85
200
13
0.065
6.6
33
465
2.6
290
37
0.13
3.6
12
460
2.6
280
53
0.19
15.5
55
3.75
3.60
4.05
4.00
3
experiment. With LEDs of different color, results obtained in
these experiments are close to the correct value, usually, to
within 6 10%.31–33 This approach raises doubts34,35 because
of the assumptions that are made. It was shown experimentally15 that the energies of photons emitted by four color
LEDs were 7%–20% smaller than the band-gap energies,
and the turn-on thresholds appeared to be significantly lower
than the photon energies. Precise values of h/e cannot be
expected from such measurements, but it is worthwhile to
look for LEDs that yield results close to the true value. In
any case, students should be familiarized with the problem.
An additional decision is the appropriate wavelength to be
used in the calculations. Usually, the wavelength relates to
the peak in the radiant power spectrum. Because the spectral
peaks are 30–50 nm wide, the uncertainty in the wavelength
may be several percent.
We used the relation
h=e ¼ VF k=c:
(4)
The VF values were found by linearly extrapolating to zero
the plots of input current versus applied voltage shown in
Fig. 2, and the uncertainty is nearly 0.05 V. The wavelengths
k were taken at the peaks in the radiant power spectra shown
in Fig. 4, and the uncertainty of these values is nearly 10 nm.
For the white LED, the wavelength is taken at the peak in
the blue part of the spectrum. However, the validity of
Eq. (4) based on the turn-on voltage remains doubtful. For
the LEDs studied, the calculated h/e values appeared to be
lower than the true value with the blue and white LEDs providing the best results. The properties of the LEDs and the
calculated h/e values are given in Table I.
IV. CONCLUSION
The experiments described here involve quantum mechanics, semiconductors, human vision, efficiency and efficacy,
optical communications, and provide good opportunities for
experimentation. The experiments are accessible to undergraduate students and can be used as laboratory exercises
and demonstrations.
ACKNOWLEDGMENT
Many thanks to Eliezer Perel for providing me with the
LEDs for the measurements and to a referee for useful
suggestions.
Yaakov Kraftmakher
829
16
a)
Electronic mail: krafty@biu.ac.il
1
M. G. Craford and F. M. Steranka, “Light-emitting diodes,” in Encyclopedia of Applied Physics, edited by G. L. Trigg (VCH, Weinheim, 1994),
Vol. 8, pp. 485–514.
2
B. G. Streetman and S. Banerjee, Solid State Electronic Devices, 5th ed.
(Prentice Hall, Upper Saddle River, NJ, 2000), pp. 379–396.
3
S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed.
(Wiley, Hoboken, NJ, 2007), pp. 601–621.
4
N. Holonyak, “Is the light emitting diode (LED) an ultimate lamp?” Am.
J. Phys. 68, 864–866 (2000).
5
S. K. Mayer, “Bringing science policy into the optics classroom: Solid
state lighting and United States lighting standards,” Am. J. Phys. 78,
1258–1264 (2010).
6
H. Kogelnik, “Optical communications,” in Encyclopedia of Applied
Physics, edited by G. L. Trigg (VCH, Weinheim, 1995), Vol. 12, pp. 119–
155.
7
J. B. Kwasnoski, “A laboratory investigation of light-emitting diodes,”
Am. J. Phys. 40, 588–591 (1972).
8
J. A. Davis and M. W. Mueller, “Temperature dependence of the emission
from red and green light emitting diodes,” Am. J. Phys. 45, 770–771
(1977).
9
J. W. Jewett, “Get the LED out,” Phys. Teach. 29, 530–534 (1991).
10
D. A. Johnson, “Demonstrating the light-emitting diode,” Am. J. Phys. 63,
761–762 (1995).
11
D. Lottis and H. Jaeger, “LEDs in physics demos: A handful of examples,”
Phys. Teach. 34, 144–146 (1996).
12
A. M. Ojeda, E. Redondo, G. González Dı́az, and I. Mártil, “Analysis of
light-emission processes in light-emitting diodes and semiconductor
lasers,” Eur. J. Phys. 18, 63–67 (1997).
13
E. Redondo, A. Ojeda, G. González Dı́az, and I. Mártil, “A laboratory
experiment with blue light-emitting diodes,” Am. J. Phys. 65, 371–376
(1997).
14
L. T. Escalada, N. S. Rabello, and D. A. Zollman, “Student explorations of
quantum effects in LEDs and luminescent devices,” Phys. Teach. 42, 173–
179 (2004).
15
J. W. Precker, “Simple experimental verification of the relation between
the band-gap energy and the energy of photons emitted by LEDs,” Eur. J.
Phys. 28, 493–500 (2007).
830
Am. J. Phys., Vol. 79, No. 8, August 2011
F. B. Seeley, A. Bandas, M. Fowler, and R. Gibson, “An inexpensive
light-emitting diode strobe system for measuring the radius of a single
sonoluminescing bubble,” Am. J. Phys. 67, 162–164 (1999).
17
P. A. DeYoung and B. Mulder, “Studying collisions in the general physics
laboratory with quadrature light emitting diode sensors,” Am. J. Phys. 70,
1226–1230 (2002).
18
Se-yuen Mak, “A multipurpose LED light source for optics experiments,”
Phys. Teach. 42, 550–552 (2004).
19
W. P. Garver, “The photoelectric effect using LEDs as light sources,”
Phys. Teach. 44, 272–275 (2006).
20
HuiYuan Opto-Electronic <www.hyledchina.com>.
21
Y. Kraftmakher, “Experiments with fluorescent lamps,” Phys. Teach. 48,
461–464 (2010).
22
PASCO <www.pasco.com>.
23
Y. Kraftmakher, “Determination of the quantum efficiency of a light
detector,” Eur. J. Phys. 29, 681–687 (2008).
24
Y. Kraftmakher, “Decay time of cathodoluminescence,” Phys. Educ. 44,
43–47 (2009).
25
OriginLab <www.originlab.com>.
26
D. C. Agrawal, H. S. Leff, and V. J. Menon, “Efficiency and efficacy of incandescent lamps,” Am. J. Phys. 64, 649–654 (1996).
27
<physics.nist.gov/cuu/Units/candela.html>
28
Y. Kraftmakher, “Telemetry in the classroom,” Phys. Teach. 41, 544–545
(2003).
29
Y. Kraftmakher, “Video through a light guide,” Am. J. Phys. 76, 788–791
(2008).
30
H. Le Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y.
Oh, “High-speed visible light communications using multiple-resonant
equalization,” IEEE Photonics Technol. Lett. 20, 1243–1245 (2008).
31
P. J. O’Connor and L. R. O’Connor, “Measuring Planck’s constant using a
light emitting diode,” Phys. Teach. 12, 423–425 (1974).
32
L. Nieves, G. Spavieri, B. Fernandez, and R. A. Guevara, “Measuring the
Planck constant with LEDs,” Phys. Teach. 35, 108–109 (1997).
33
F. Zhou and T. Cloninger, “Computer-based experiment for determining
Planck’s constant using LEDs,” Phys. Teach. 46, 413–415 (2008).
34
D. F. Holcomb, “LEDs: Their charm and pitfalls,” Phys. Teach. 35, 198 (1997).
35
R. Morehouse, “Answer to Question #53. Measuring Planck’s constant by
means of an LED,” Am. J. Phys. 66, 12 (1998).
Yaakov Kraftmakher
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