Doulbe Slit Diffraction
-
Upload
bronwyn-reid-oconnor -
Category
Documents
-
view
231 -
download
0
Transcript of Doulbe Slit Diffraction
-
8/9/2019 Doulbe Slit Diffraction
1/13
EXPERIMENT 1: DOUBLE-SLIT DIFFRACTION
AND DIFFRACTION GRATINGS
AIM:
1. To perform the classic Youngs experiment, in which the diffraction of light by
a double slit is observed.2. To measure the slit width and slit separation using diffraction.
3. To use computer simulation in diffraction problems.
INTRODUCTION:
In approximately 1805, Thomas Young performed an experiment which showed that
light exhibits properties simular to waves. The results from Youngs experiments have
resulted in widely accepted knowledge regarding the behaviour of light.
When a beam of light with wavelength is incident towards a barrier with a single slit in
it, the light will diffract in a pattern similar to the figure below. Each of these propagating
waves can be considered to act as a point source (Huygens-Fresnel Principle).
Fig. 1.1http://electron9.phys.utk.edu/phys136d/modules/m9/diff.htm
When the cumulative effects of multiple slits and wavefronts are considered, the
individual wavefronts will interfere so that when two peaks of a wavefront meet, the
amplitude of the wave is enhanced (increased) and when a peak and a trough meet, the
amplitude of the wave is partially or totally cancelled (decreased). Essentially, the
wavefronts either interact constructively or destructively.
http://encyclozine.com/science/physics/waves http://www.sciencestudy.org/post/Interference.aspx
When the interference patterns from slit experiments are observed on a screen,
constructive interference results in bands of bright light and deconstructive interference
results in a band of darkness separating the illuminated sections.
PICTURE
http://electron9.phys.utk.edu/phys136d/modules/m9/diff.htmhttp://encyclozine.com/science/physics/waveshttp://encyclozine.com/science/physics/waveshttp://www.sciencestudy.org/post/Interference.aspxhttp://electron9.phys.utk.edu/phys136d/modules/m9/diff.htmhttp://encyclozine.com/science/physics/waveshttp://www.sciencestudy.org/post/Interference.aspx -
8/9/2019 Doulbe Slit Diffraction
2/13
Minima (I = 0)
Order of minima (m) = 1
The intensity of the bands of light can be qualitatively described by the function:
2
2
2
0 cos.sin
),( II =
Where 0I = the central intensity, = kb sin , b = slit width, = 1/2kd sin , d =
slit separation and k=2/.
The intensity of a beam of light, or amplitude squared, is a way of measuring the energy
emitted by a light source which is not perceivable to the human eye.
A single slit diffraction pattern is described by 2
2sin
and 2cos is the diffraction
pattern due to double slits.
http://www.sparknotes.com/physics/optics/phenom/section2.rhtml
The red line in the figure above shows the diffraction pattern of a single slit experiment.
Atb
, the first minima occurs (a band of darkness would be observed at
b
=sin
). This red line encloses another plot (seen in blue) and this is the double slit diffraction
pattern.
The minima in 2
2sin
occur when 0sin = . Therefore = for the first positive
minimum.
as = kb sin :
Central Intensity (I0)
http://www.sparknotes.com/physics/optics/phenom/section2.rhtmlhttp://www.sparknotes.com/physics/optics/phenom/section2.rhtml -
8/9/2019 Doulbe Slit Diffraction
3/13
sin2
1kb=
sin
2
2
1b=
sinb=
sin=b
The minima in 2cos occur when cos =0. Therefore, =2
,
2
3
=
2
1m where m is the order of the minimum.
as = sinkd :
sin2
1
2
1kdm =
sin
2
2
1d=
sind=
sin1
2
1dm =
sin2
1dm =
sin
2
1
=m
d
APPARATUS:
-
8/9/2019 Doulbe Slit Diffraction
4/13
Class 2 laser, 1mW output, =632.8nm.
Optical bench
Slide mount
1 x double slit optical slide
2 x optical slides with 4 slits
Screen
PROCEDURE:
1. Set up the apparatus as shown in the diagram below.
2. Fixed the slide mount and screen by locking them to the optical bench.
3. Measured and recorded the distance from the slide mount to the screen
4. Turned on the laser so that the centre of the beam could be seen on the screen.
5. Carefully marked the position of the beam on the screen.
6. Measured and recorded the distance from the centre of the beam to the edge of the
screen.7. Calculated the maximum value of and sin based on the above measurements.
8. Mounted slide 1 and adjusted vertically and horizontally until the laser diffracted
through a single slit evenly and clearly (single slit diffraction).
9. Marked the first minima either side of the centre of the beam (from = 0).
10. Measured and recorded the distances of the minima from the centre in table 1 and
calculated .
11. Mounted slide 2 and adjusted vertically and horizontally until the laser diffracted
through double slit pattern 1 evenly and clearly (double slit diffraction).
12. Marked the single-slit minima and the first 10 minima either side of the centre ofthe beam (from = 0).
13. Measured and recorded the cumulative distance of each minimum from the
centre of the beam in table 2.
14. Repeated steps 11 - 13 for pattern 2 on slide 2 and for pattern 3 on slide 3.
15. Calculated the average value of for the single-slit minima.
16. Calculated b.
17. Used the CUPS program to model a single-slit diffraction pattern using the same
experimental values forb and .
18. Found the angle corresponding to the first minima on CUPS and compared to the
experimental calculation
19. Plotted sin m against
2
1m for (m, m ) > 0 and sin m against
+
2
1m for
(m, m ) < 0 in graph 1for all three double-slit diffraction patterns.
20. Calculated dfor each double slit pattern from the gradient of each line in graph
1.
21. Used the CUPS program to model a double-slit diffraction grating using the d
values calculated for each double-slit pattern.
22. Recorded the angles for the first five simulated minimums and compared to the
experimental values in table 3.
23. Used the CUPS program to model slit patterns from three slits to 10 and found apattern between the number of slits and shape of the graph.
-
8/9/2019 Doulbe Slit Diffraction
5/13
W
L
RESULTS:
Measurements:
Distance between slide mount and screen: L = 1.335 m 0.0005m
Distance from central beam to edge of screen: W= 0.145 m 0.0005m
Laser beam wavelength: = 632.8 nm
Calculation of :
= L
W1tan
=
335.1
145.0tan 1
o199.6=
108.0= radians
10779.0)108.0sin(sin ==
sin
For ease of calculations, it will be assumed that sin for the remainder of thecalculations.
Table 1: Single-Slit Minima
-
8/9/2019 Doulbe Slit Diffraction
6/13
Distance from central beam to first
order minima (all values are )
sin (radians)
(all values are )
Single Slit Diffraction 4.0cm
335.1
040.0tan 1 = 0.030
Double Slit Diffraction:
Slide 2-1
3.9cm
335.1
039.0tan 1 = 0.029
Double Slit Diffraction:
Slide 2-2
3.4cm
335.1
034.0tan
1= 0.025
Double Slit Diffraction:
Slide 3-3
3.9cm
335.1
039.0tan 1 = 0.029
Average 0.028
Error in length measurements = 0.0005m
Calculation of Error for :
Variation of about the mean =
2
minmax
=
2
0.025-0.030
= 0.0025 radians
0025.0028.0 = radians
Calculation ofb:
Where = 632.8 0.05nm and sin = 0.028 0.0025 radians
sin=b
028.0
108.632 9=b
5103.2 = m
023.0= mm
Computer Simulation of Single Slit Minima:
When b = 0.021 and = 623 nm:
-
8/9/2019 Doulbe Slit Diffraction
7/13
sin = 1.75o = 0.030 radians
Comparison of experimental value of and CUPS value of for single-slit minima:
029.02
028.0030.0
2=+=+= ALEXPERIMENTCUPS
AVERAGE radians
001.0029.0 = AVERAGE radians
Experimental Error =
-
8/9/2019 Doulbe Slit Diffraction
8/13
Slide 2, Slit 1 Slide 2, Slit 2 Slide 3, Slit 3
Order
Distance from
centre (m)
(radian
s)
Distance from
centre (m)
(radian
s)
Distance from
centre (m)
(radian
s)
-10 -0.079 -0.059 -0.050 -0.037 -0.026 -0.019
-9 -0.070 -0.052 -0.046 -0.034 -0.023 -0.017
-8 -0.062 -0.046 -0.040 -0.030 -0.021 -0.016
-7 -0.053 -0.040 -0.036 -0.027 -0.018 -0.013
-6 -0.045 -0.034 -0.032 -0.024 -0.015 -0.011-5 -0.037 -0.028 -0.022 -0.016 -0.013 -0.010
-4 -0.028 -0.021 -0.017 -0.013 -0.010 -0.007
-3 -0.019 -0.014 -0.013 -0.010 -0.007 -0.005
-2 -0.012 -0.009 -0.007 -0.005 -0.004 -0.003
-1 -0.004 -0.003 -0.002 -0.001 -0.002 -0.001
0 0.000 0.000 0.000 0.000 0.000 0.000
1 0.004 0.003 0.002 0.001 0.002 0.001
2 0.012 0.009 0.007 0.005 0.004 0.003
3 0.019 0.014 0.013 0.010 0.007 0.005
4 0.028 0.021 0.017 0.013 0.010 0.007
5 0.037 0.028 0.022 0.016 0.013 0.010
6 0.045 0.034 0.032 0.024 0.015 0.011
7 0.053 0.040 0.036 0.027 0.018 0.013
8 0.062 0.046 0.040 0.030 0.021 0.0169 0.070 0.052 0.046 0.034 0.023 0.017
10 0.079 0.059 0.050 0.037 0.026 0.019
Table 2: Double Slit Diffraction
-
8/9/2019 Doulbe Slit Diffraction
9/13
Graph 1:
Double Slit Diffraction: Slide 2, Slit 1
y = 0.0062x + 4E-18
R2
= 0.9998
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
-10 -5 0 5 10
(m-1/2) for (m,)>0 and (m+1/2) for (m,)
-
8/9/2019 Doulbe Slit Diffraction
10/13
Graph 2:
Double Slit Diffraction: Slide 2, Slit 2 y = 0.004x - 3E-19
R2 = 0.9981
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
-10 -5 0 5 10
(m-1/2) for (m,)>0 and (m+1/2) for (m,)
-
8/9/2019 Doulbe Slit Diffraction
11/13
Graph 3:
Double Slit Diffraction: Slide 3, Slit 3 y = 0.0021x + 5E-19
R2 = 0.9995
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.030
-10 -5 0 5 10
(m-1/2) for (m,)>0 and (m+1/2) for (m,)
-
8/9/2019 Doulbe Slit Diffraction
12/13
Calculation ofd:
sin
2
1
=m
d
as5.0
sin
m
is the gradient in graph 1, 2 and 3:
gradientd
=
Slide 2, Double Slit Pattern 1:
Where 181040062.0 += xy :
0062.0
108.632 9
1.2
==gradient
d
41002.1 = m
102.0= mm
Slide 2, Double Slit Pattern 2:
Where 19103004.0 = xy
004.0
108.632 9
2.2
==gradient
d
41058.1 = m
158.0= mm
Slide 3, Double Slit Pattern 3:
Where 191050021.0 += xy
0021.0108.632
9
3.2
==gradient
d
4103 = m
3.0= mm
-
8/9/2019 Doulbe Slit Diffraction
13/13
Table 3: Comparison of Computer Simulation Minima to Experimental Values:
Slit 2, Pattern 1 Slit 2, Pattern 2 Slit 3, Pattern 3
Order Minima
(degrees)
Minima
(radians)
Minima
(degrees)
Minima
(radians)
Minima
(degrees)
Minima
(radians)
1 0.34 0.006 0.180 0.003 0.110 0.002
2 1.05 0.018 0.530 0.009 0.330 0.006
3 1.67 0.029 0.850 0.015 0.580 0.010
4 2.32 0.040 1.170 0.020 0.760 0.013
5 1.500 0.026 0.990 0.017
Slit Seperation (d)