doulbe slit diffraction

8/9/2019 Doulbe Slit Diffraction

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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


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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


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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:


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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.


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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


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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


Slide 2-2

3.4cm

335.1

034.0tan

1= 0.025


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:


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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 =


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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


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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,)


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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,)


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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,)


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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


Where 19103004.0 = xy

004.0

108.632 9

2.2

==gradient

d

41058.1 = m

158.0= mm


Where 191050021.0 += xy

0021.0108.632

9

3.2

==gradient

d

4103 = m

3.0= mm


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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)

doulbe slit diffraction

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