modern optics lab lab 7: diffraction and interference experiments slit width and slit separation...

$: Modern Optics Lab Lab 7: Diffraction and Interference Experiments Slit width and slit separation dependence of diffraction pattern for single and double$
Modern Optics LabLab 7: Diffraction and Interference Experiments

Slit width and slit separation dependence of diffraction pattern for single and double slits in the Fraunhofer (far-field) regime.

Babinet’s principle: Determine the thickness of your hair.

Diffraction pattern for circular apertures.

Quantitatively measuring the intensity distribution of the diffraction patterns of single and double slits in the Fraunhofer (far-field) regime and fitting data to theory.

Determination of the ration of slit-width a and slit separation-distance d from the double slit diffraction pattern.

Topics


VII.A Experiments with the Observation Screen

Look at single slit diffraction pattern for different slit widths.

Determine the laser wavelength from the diffraction pattern minima from a single slit.

x

I(x)

L

...3,2,sin :occur when Minima

a

2

2

0

sin

sinsin)(

a

a

II


Babinet’s PrincipleThe diffraction pattern in the far field due to a given screen is the same as the diffraction pattern due to it’s complement.Translation for our experiment:A slit of width a produces the same diffraction pattern as a hair of the same width.

x

I(x)

L

...3,2,sin :occur when Minima

a

2

2

0

sin

sinsin)(

a

a

II


VII.A Determine the Thickness of your Hair

View from the frontTape hair to component holder

Laser beam should hit the hair


VII.A Diffraction pattern of a small circular aperture

View from the front

Use the slide that contains circular apertures of sizes 0.04mm and 0.08mm (those you should use). It also contains a big square and a big round hole with patterns inside.


VII.A Diffraction pattern of a small circular aperture

For circular aperture (a hole) of diameter q the diffraction pattern is an “airy disk”.


Mathematical Description of the Diffraction Pattern of a Circular Aperture in the Far-Field

2

1

0

sin2

sin2

2

a

aJ

IIJ1 = “Order One Bessel Function”

.....,832.3sin2

0sin

2

sin2

0 when Minima

1

aa

aJ

I



aperture) ofdiameter (q

22.1832.3

ringdark first for the 832.3sin2

q

q

a


Angle of first minimum (dark circle) (measured from axis that goes through center of the central bright disc):

Small angle approximation ( in radians)



69.3238.3

679.2233.2

635.1220.1

0

Maxima Minima

aperture ofdiameter q where, m

sin

:minima and maxima More

m

m

m

m

q


VII.B Experiments with Linear Translator,…….

Observe the diffraction pattern intensities at your setup using the linear translator, photometer, and oscilloscope.

Record patterns using translator, photometer, noise filter, 750 interface, and Data Studio at the front table and email the results to yourself.

Process the measured intensity pattern with Excel and generate a theoretical intensity pattern in Excel.

Compare measured and theoretical pattern in a graph in Excel.


VII.B Example of Processing Single Slit Data in ExcelTime Voltage Time-tc Voltage-Voffset I(t)

0 1.1 -25

1 1.1 -24

2 1.1 -23

3 1.2 -22

….. ….. ……

From Data Studio

Calculate from “Time”-column(Time-tc=0 at peak of pattern)

Calculate from “Voltage”-column(so that Voltage-Voffset goes to zero at the edges of the pattern.

Calculate the theoretical Intensity distribution.


VII.B Calculating I(t)

D

aA

Avt

AvtItI

where,

)sin()0()(

2

You can read that off your data (Voltage-Voffset at the maximum intensity)

D = distance from the slit to the fiber optic cablea = slit width=632.8nm

v = 10mm/min

t = Time - Toffset


VII.B Hints for getting the ratio of slit width a and slit separation d for the double slit from the diffraction pattern.

Double slit maximamdouble=1,2,3

Single slit minimummsingle=1


Double slit maximamdouble=1,2,3

Single slit minimummsingle=1

d

doublemsin :maximaslit Double

a

singlemsin :minimaslit Single

modern optics lab lab 7: diffraction and interference experiments slit width and slit separation...

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