Planck's Constant

Purpose:
  The objective of this lab was to verify Planck's constant by essentially messing around with two LEDs.

Note: this lab was completed very quickly after class and the opportunity for photographs was very scarce.  Only one unclear photograph was collected.  

  The wavelength that each LED projects was found.  And the Voltage across each LED was also measured.  Next the wavelength was graphed versus 1/E.     Furthermore, the graph suggest that the slope is h*c , where c is the speed of light.  Thus diving by c should yield Planck's constant. Note multiplying the voltage by charge gives one energy.

For the first LED, 1.95 volts and a wavelength of 590 nm (yellow) were measured.
For the second LED, 2.76 volts and a wavelength of 450 nm (blue) were measured.

 Note this graph is not very good since this lab was done as a class at a very fast pace.  


Since the graph is not very clear, the slope will be calculated manually.
-->  rise/run = h*c --> h = 3.1(10^-15) ev*s.

Multiplying by 1.6 (10^-19) J/1 ev yields --> 4.96 (10^-34) J*s.

This is not too far from the accepted value 6.63(10^-34) J*s.  The percent error is very large at 25%. However the error stems from the equipment.  If more time was given for completion of the lab, more LED lights would have been subject to test.  Inevitably this would have produced a much better slope.  Nonetheless all things considered, the degree of magnitude is the same.

Color and Spectra

The purpose of this experiment is to view the spectrum of colors found in white light and to measure the corresponding wavelengths for each color observed in the spectrum. Moreover, this experiment was is consolidated from three parts.  For part one, two and three, the light source is an incandescent lamp, the light source stems from an unknown source, and the light source emanates from hydrogen gas respectively.  For the second part the unknown will be identified.

Above: The Set up--This set up was used for all cases.


Note two one-meter stick were used and a defraction grating.


The relevant equation used is lambda = D x d/(L^2 +D^2)^(1/2) 
where d is fixed and = 500 slits/mm =2 micro meters and L is the distance from the defraction grating to the light source and D is the distance from the color of interest on the light spectrum to the light source. 



Part 1:

Note: the uncertainty in all the distances D is +/- .1 cm and the uncertainty for L is +/- 1cm

The data collected for the first experiment is presented in the above photograph. The lambda prime equation is derived essentially from solving two unknowns--the slope and the constant--from two equations: lambda prime = m*lambda+ constant for violet and lambda prime= m*lambda + const  for red.  For the first equation, the lambda prime is replaced by lowest boundary for violet--roughly 390nm-- in the visible spectrum for humans and the value for lambda is the one that was calculated for the experiment (see above photograph).  The same idea is used for the second equation. However this time the highest boundary for red in the visible spectrum for humans is used for lambda prime.  


Lambda prime values (nm):
1 = 389 +/- 6.0
2 = 447 +/- 6.5
3 = 540 +/- 7.5
4 = 592 +/-  8.0
5 = 668 +/- 8.8
6 = 749 +/- 9.6    all of these lambda primes are within the uncertainty

Part 2:
For part two, an unknown gas number one was given.

It should be noted that the length L changed and that the uncertainty values for D and L are +/- .1 cm and +/- 1 cm respectively.























All the data is observed in the above photograph.  Moreover, the unknown was determined to be mercury Hg.  Only three colors were observed in the spectrum and they were green, yellow-orange-like color, and blue. These values correspond to lambda-1, lambda-2, and lambda-3 respectively in the above photograph.  Nonetheless, it was determined that the source was mercury through a reliable internet source that had the visible spectrum of mercury that matched the data in the above photograph.  


Part 3:

Note that the uncertainty for D is +/- .1 cm and the uncertainty for L is +/- 1 cm.


There were only three distinct visible lights in the visible spectrum for the hydrogen gas. All the necessary data was found and presented in the above photograph.  Moreover, the corresponding energies E-1, E-2, and E-3 are 4.87(10^-19) J, 4.13(10^-19) J, and 2.98(10^-19) Joules respectively.

CD Diffraction

The purpose of the experiment is to measure the distance d between the grooves on a CD for the Easy Listening Music Studio company.

This is accomplished by allowing a Helium Neon Gas Laser--which has a wavelength of 630 nm--to strike the disk normally.  As a result the first and second order maxima appear on the screen or white board.

(Above: The Set Up)


The distance from the slits or groves to the screen is a distance L 51 +/- 1 cm.  Moreover after the experiment was conducted, the lengths of the first and second-order maxima to the zeroth-order maxima are x-1 22.5 +/- .5 cm and x-2 68.8 +/- .5 cm respectively.  These values were used to find the relative angles, atan (x/L) = theta.


Calculations:

Key Equation: d*sin(theta) = m*lambda , where m is the maxima number and d is the distance between the grooves.

Note that the d set equal to 51 cm in the above photograph is really L, the distance from the slit to the screen or whiteboard.  Also the second equation should be multiplied by two since it is the second-order  maxima, m=2.  

Lenses

The purpose of the experiment is to ultimately verify the relationship between the focal length f, image distance D-i, and object distance D-o by exploring converging lenses.

To begin, one had to measure the focal length of the lense and this was accomplished by using an infinite light source--the sun.  The focal length was distance between the lense and the sharp point on the surface where all the sun rays collected.  The focal length was measured to be 20 +/-1 cm.

Once that was accomplished, the lense was placed four focal lengths--D-o equals 80 +/- .5cm--away from an object--a filament--that had a height of 9 +/-.5 cm ( one should keep in mind that there is a light source emanating from the object. See picture below). 
     

The height of the image H-i was measured to be 3 +/- .5 cm and the image distance D-i equals to 25 +/- .5 cm.   It is very important to note that image being projected is real and inverted.  Nonetheless, the lense was flipped around so the light of the object enters the other side.  This change did not produce any new data that was not already known.  That is to say that the image was still real and inverted. The image distance and height were remained the same as well.  The magnification was .49 +/-.091.

The lense was then moved to 2 focal lengths:
D-o = 40 +/- .5 cm H-o = 9 +/- .5 cm
D-i = 36 +/- .5cm   H-i = 8.5+/- .05 cm
M = .94 +/- .058

*After flipping the lense again, nothing was changed--all numbers are the same and the image was still real and inverted.

The lense was then moved to 1.5 focal lengths:
D-o = 30 +/- .5 cm H-o = 9 +/- .5 cm
D -i = 52 +/- .5 cm H-i = 16 =/- .5 cm
M = 1.78 +/- .153
*Once again the image was real and inverted and numbers did not change after flipping the lense.


The next part of the experiment consisted of applying the same technique of moving the lense to various distances from the object. The object was no longer the fillament but a small key chain that had the form of a bear.  The following data was obtained.

 

Object distance (cm)		Image distance (cm)		object height (cm)	image height (cm)	M	Type of image
5f		23 +/- .5		5.1 +/- .05	1.7 +/- .05	0.333 +/- .0131	real,inverted
4f		24.5 +/- .5		5.1 +/- .05	2 +/- .05	0.392 +/- .0136	real, inverted
3f		28 +/- .5		5.1 +/- .05	2.5 +/- .05	0.49 +/- .0057	real, inverted
2f		32 +/- .5		5.1+/- .05	3.2 +/- .05	0.627 +/- .0159	real, inverted

 

The image is real and inverted.

The graph above is one over the image distance versus negative one over the object distance.  The y-intercept represents one over the focal length 1/f.  Initially the focal lenth was measured to be 20 +/- 1 cm.  However with respect to the graph, the focal length is 19.69 cm.  This yields a percent difference 1.5 percent which is within error range.  More importantly the lab supports the idea that 1/D-i + 1/D-o = 1/f.

Concave and Convex Mirrors

The objective of this experiment is to explore the images formed by convex and concave mirrors.  

CONVEX MIRROR:

For a convex mirror the object appears larger than the image and is upright.  If one moves the object closer to the convex mirror, then the image becomes a bit larger but still smaller relative to the size of the object.  The image also gets a little bit closer.  Moreover if  object moves farther away from the convex mirror, then the image gets smaller, the image is farther away, and remains upright.

The convex diagram is an emblem of the observation made during the activity.

For Convex Diagram (left):
height of object Ho= .031 meters
height of image Hi = .007 meters
Distance of object Do = .062 meters
Distance of image Di = -.019 meters

Magnification M = Hi/Ho = .226

CONCAVE MIRROR:

For the concave mirror, the image is inverted and much larger than the object.  When the object is retreated to a large radius, the object remains inverted and becomes larger.  However if the object is moved close enough to the concave mirror, the image becomes up right and smaller.

This concave diagram is a representation of the observations made during the activity.

For Concave Mirror (left):
Ho = .031m
Hi = -.007 m
Do = .113 m
Di = .023 m

M = Hi/ Ho = -.258

Measuring the Length of a Pipe with Standing Waves?

The purpose of this lab was to measure the length of an open pipe by swinging it around and creating standing waves.  A microphone connected to a sensor was positioned near the swinging pipe and recorded all necessary data--omega specifically.

Although it may not be distinguishable in the photograph, omega equals to 3859 rad/s for the first case. Hence for the first case f-1 roughly equals to 614 hz.

 Again it may not be distinguishable in the photograph, but for the second case, omega = 5068 rad/s.
Therefore f-2 equals 806 hz.

From here, there are three equations and three unknowns.  (eq1) f-1 = (n-1*V)/(2L)
(eq2) f-2 = (n-2*V)/(2L)               (eq3) n-2 = n-1 +1

After solving for the wanted unknown length of the pipe L, one gets .837 meters.

Introduction to Sound

The purpose of the experiment was to become familiar with sound and it's characteristics lambda, period T, frequency f, and amplitude A by saying "AAAAAA" into a microphone connected to a sensor.

After saying "AAAAA" into the microphone, the wave projected has a periodic pattern--see above photograph and in large if needed.  Specifically there were three waves captured by the sensor in the small time interval.  And the period T was determined by diving the time interval by the number of waves.  This number was .009 Sec.  From here the frequency of the sound was determined 1/T = f which was 111.11 hz. The assumption is that the speed of sound is 340 m/s in the room.  From here, the wavelength was determined to be 3.06 meters.  The amplitude A was determined by subtracting the lowest peak of the wave from the zenith point of the pattern and diving that by two.  The highest point was 2.594  and the lowest point is 2.620.  This yields an amplitude of 0.167 m.  Moreover if data was collected for an "AAAAA" sample that was 10-times-longer time interval, the data might change a little bit because of damping.  That is to say that the wave will fall off some because one's "AAAAA" may not be uniform over the entire time frame.  If the "AAAAA" is quieter as time increases, then amplitude will become smaller.  This is the case because the amplitude of the wave is proportional to the magnitude of the noise.