Download Experiment 1: Fraunhofer Diffraction of Light by a Single Slit

Experiment 1: Fraunhofer Diffraction of Light by a Single Slit
Purpose
1. To understand the theory of Fraunhofer diffraction of light at a single slit and at a
circular aperture;
2. To learn how to measure the intensity distribution of the diffracted light by a single
slit;
3. To learn how to measure the radius of the wire by the diffraction method.
Apparatus
Laser, diffracting objects (including a single slit, a circular aperture, a wire), lens,
photocell, resistance box, MCDF20 single slit diffraction set, oscilloscope
Theory
"Diffraction" refers to the spreading of waves and appearance of fringes that occur
when a wave front is constricted by an aperture in a screen that is otherwise opaque.
The Huygens-Fresnel principle governs diffraction phenomena: "Every unobstructed
element of a wavefront acts as a source of spherical waves with the same frequency as
the primary wave. The amplitude of the optical field beyond is a superposition of all
these wavelets taking account of their amplitudes and phases." When both the light
source and the viewing plane are effectively at infinity with respect to the diffracting
aperture，In this case, the incident light is a plane wave so that the phase of the light at
each point in the aperture is the same. The phase of the contributions of the individual
wavelets in the aperture varies linearly with position in the aperture, this is the
Fraunhofer approximation. In practice the diffraction pattern is viewed at a long
distance from the diffracting object, or at the focal plane of an imaging lens.
1. Fraunhofer diffraction at a single slit
Alternately dark and bright fringes will be observed at the viewing plane when parallel
light is diffracted by a single slit. As shown in Fig. 1, the Fraunhofer diffraction
pattern has maximum intensity at the central location which is determined by the
rectilinear propagation law of light, and a series of peaks of decreasing intensity and
width on each side symmetrically. The intensity distribution of the diffracted light,
is given by
where
is the width of slit,
is the diffraction angle,
is light wavelength, and A
is a factor for maximum intensity. The pattern is shown in the image together with a
plot of the intensity vs. angle θ. Most of the diffracted light falls between the first
order minima (Fig. 1).
Two conclusions can be drawn herewith
(1) Dark fringes correspond to zero intensities of the diffracted light, i.e.
(2) Diffraction angles corresponding to secondary maxima are determined by
with normalized light intensities of
respectively.
Figure 1: The Fraunhofer diffraction pattern
2. Fraunhofer diffraction at a circular aperture
The Fraunhofer diffraction pattern given by a circular aperture is characterized by
concentric circles. The concentric intensity distribution of the diffracted light,
given by
In which
and b is the radius of the aperture.
is
It can be seen that most of the light is in the central disk. The angle subtended by this
disk, known as the Airy disk, is determined according to the formula of
.
3. Diffraction by objects with mutually complementary shapes
Consider two diffracting bodies with mutually complementary shapes, let A be the
original one, and B its complement, i.e. the body that is transparent where A is opaque,
and opaque where B is transparent. Suppose
and
are electric fields for
diffracted light by A and B on the surface of the viewing plate,
because no diffracted light can reach to the viewing plate if both A and B are
assembled, therefore,
. This means that the sum of the radiation
patterns caused by A and B must be the same as the radiation pattern of the
undisturbed beam. In places where the undisturbed beam would not have reached, this
means that the radiation patterns caused by A and B must be opposite in phase, but
equal in amplitude, this is the Babinet's principle. Diffraction patterns from apertures
or bodies of known size and shape are compared with the pattern from the object with
equivalence in size and shape to be measured. Consequently, diffraction pattern of a
single slit with a width of a is usually used to detect the diameter a of a wire.
Experiment
As shown in Fig. 2, a monochromatic laser beam is used as the incident light. The
intensity of the diffracted light is measured with a photodiode or a CCD.
Figure 2: Arrangement for Fraunhofer Diffraction
1. Light intensity detection by a photocell
The shot-circuit current (photocurrent) of the silicon photocell is proportional to the
incident light intensity. The detector will be shifted in the direction perpendicular to
slit during the experiment, in order to measure light intensity distribution in the
observation screen.
Weak photocurrent is determined by recording the deflection amplitude, which is also
proportional to the light intensity, of the light spot on the transparent window of a
galvanometer. Tune the hand screw to slide the photocell and analyzing slit along a
calibrated translation stage so that the detailed shape of the diffraction pattern can be
discerned. By carefully shifting the detector, central bright fringe can be located. The
revolution counter reading
at this point is taken as the origin. By adjusting a load
resistor or adjusting slit width, the initial division reading
of the galvanometer is
set to be about 80. The photocell should be shifted to one side (either left side or right
side) at first, so as to ensure that all the intensities near the central maximum will be
recorded in the following measurement. Begin intensity measurement in a 0.2mm step,
record both the position and the intensity readings x, n, until the secondary dark fringe
is covered. Be sure to tune the screw always in one direction during measurement, in
order to avoid inaccuracy of position readings caused by the backlash errors of the
actuating mechanism.
2. Light intensity detection by a CCD detector
As shown in Fig. 3, the measuring system includes laser, analyzing slit, CCD detecting
set and oscilloscope, etc. The CCD detecting set consists of a pair of polarizers, CCD
detector, driving circuit, signal processing unit and power supply. The polarization
direction of polarizers, one of which is fixed, and another is adjustable, can be
adjusted to attenuate light that is incident on the CCD detector.
The signal output of CCD is a chain of electric pulses corresponding to light
intensities (in form of voltages) generated by each pixels. After amplification and
filtering, time-dependent voltage signal is generated in sequence of the pixel order. An
one-dimensional spatial distribution of the diffracted light can be displayed in the
mode of T-V on the oscilloscope.
Figure 3: Intensity detection using CCD
Essentials of adjustment
(1) Connection of an oscilloscope to the measuring system
A dual-channel oscilloscope is used in experiment. Connect the output end
labeled
“signal” of the measuring system to “CH1”, another one labeled “Trigger” to
“CH2” in the instrument. Set the triggering level, the scale divisions for “CH1”, “CH2”
and time properly so that stable triggering pulses can be fully displayed on both sides
of the observation screen of the oscilloscope.
(2) Light path adjustment
Align the laser, slit and CCD detector to be equal in altitude and coaxial. With the
laser on, carefully adjust the polarizer until the diffraction pattern is clearly visible on
the entrance window of CCD detector.
Further adjustment may be required in order
to display the intensity distribution of the diffracted light on the oscilloscope. Locate
the central peak right in the middle on the screen. If the intensity curve turns to be
flattened out in case of too strong incident light, the polarizer should be rotated
gradually again, in order to reduce light irradiance on the photosensitive surface of
the CCD.
(3) Measurement of light intensity
The curve displayed on the screen of the oscilloscope corresponds to relative intensity
distribution. Take note of the coordinates on the distribution curve at 15-20 arbitrary
transverse positions and convert them into spacing. Measure the distance
between
the slit and the CCD detector. Draw a line chart showing the relationship of relative
intensity to the diffraction angle, i.e.

, on graph paper.
Caution:
1. Avoid direct incident of laser beam on the CCD detector.
2. Carefully clean the polarizers in a way similar to optical lens cleaning and do not
touch them directly with your fingers or hands.
3. Carefully change the polarization direction by gradually and slowly rotating the
polarizer during experiment.
Primary requirements
1. Use photocell to detect the diffracted light, measure photocurrents of the photocell
at different locations from the central maximum to the secondary bright stripe.
Draw a graph of

, and calculate the slit width a. Repeat the measurements
to get the average value of a. Compare the averaged slit width a with that measured
by means of a reading microscope.
2. Use CCD as a detector, observe the diffracted light distribution pattern on an
oscilloscope, record experimental data and draw a graph of

. Compare a
once again.
3. (optional) Try to get the diffraction pattern of the circular aperture, determine the
position for the first minimum (i.e. the radius of the Airy disk), and, finally,
calculate the radius of the circular aperture.
4. (optional) Try to measure radius of a thin wire by means of the diffraction method.
Problems
1. What kind of influence on the diffraction pattern to be expected when factors such
as width and orientation of the single slit, and distance of the viewing plate away
from the slit are concerned?
2. If red and blue lights are used simultaneously, will their central maxima overlap?
And will the secondary bright fringes overlap? Give reasons.
3. What kind of influence on the diffraction pattern to be expected when wavelength
of the incident light is too long or too short?