Diffraction of microwaves
DEP
Related topics
Microwaves, electromagnetic waves, Huygens-Fresnel principle, double-slit, diffraction
Principle
According to the Huygens-Fresnel principle, electromagnetic waves will be diffracted at an
aperture or obstacle, and a characteristic intensity pattern can be observed at a certain
distance behind this object.
Note
Prior to performing this experiment, it would be helpful, though not mandatory, to perform
the experiment P2460510 "Standing waves in the microwave range" first.
Equipment
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Microwave set 11742-93
Microwave transmitter
Microwave receiver
Microwave probe
Microwave control unit
Meter rule
Angle scale
Double-slit
Cover plate
Additional equipment
Multimeter ADM1, demo., analogue
Connecting cord, 32 A, 750 mm, red
Connecting cord, 32 A, 750 mm, blue
Barrel base PHYWE
Support rod, stainless steel 18/8, l = 250 mm, d = 10 mm
Boss head
Vernier calliper, stainless steel
13810-01
07362-01
07362-04
02006-55
02031-00
02043-00
03010-00
Fig. 1: Set-up for diffraction experiment
Tasks
Familiarise yourself with the phenomenon of diffraction through a single-slit and on a small
obstacle.
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DEP
Diffraction of microwaves
Theory
If a diffraction object, e.g. a slit, double-slit, or grating, is placed in the beam path of a
source of light, an intensity pattern, which is characteristic of the object that is used, can
be observed at a certain distance behind this object. This is due to the diffraction of the
light on the edges of the object. This phenomenon can be explained by way of the
Huygens-Fresnel principle according to which every point of the object edge is considered
the starting point of a new wave. When the waves interfere with each other at a distant
point (interference), the result is an intensity profile that cannot be explained by way of
geometrical projection (shadow-casting) (no consideration of the diffraction effects).
Therefore, proof of interference is also proof of the wave nature of light (here: of light in
the microwave range).
However, the relationship described above applies only if the so-called far-field
approximation is used: Only if the distance between the aperture and the location of the
intensity measurement (here: between the double-slit and receiver) is sufficiently long can
the diffraction effects on the slit on which the interference is based be sufficiently
developed.
In order to estimate as to whether far-field approximation can be applied to an experiment
set-up, the so-called Fresnel number F is defined:
F=
b2
d⋅λ
(1)
Here, b is a characteristic size of the aperture (here: width of the slit b) and d is the
distance between the aperture and the location of the intensity measurement
(wavelength λ). The Fresnel number is a dimensionless number. Far-field approximation is
fulfilled if:
F≪1
(2)
This is why it must be ensured that the distance d of the receiver from the double-slit is not
too small, since it is incorporated into the Fresnel number in a reciprocal manner.
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Diffraction of microwaves
DEP
Set-up and procedure
First experiment: Diffraction through a slit
Set the experiment up as shown in Fig 2.
Fig. 2: Experiment set-up
Connect the microwave transmitter and receiver to their associated sockets of the control
unit. Connect the multi-range meter to the voltmeter output of the control unit and select
the 10 V measuring range (direct voltage). Set the amplitude controller to maximum. The
loudspeaker and internal or external modulation are not required for this part of the
experiment.
Combine the angle scale and meter rule by way of the screw on the back of the angle scale
and the recess in the meter rule. Set the mark of the scale to 180°. Turn the meter rule in
order to align the reference mark (arrow) on the angle scale with the one of the meter rule
so that they coincide (see Fig. 3).
Fig. 3: Set-up and alignment of the angle scale and meter rule
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Diffraction of microwaves
Fig. 4: Single-slit in the microwave beam
Install the double-slit in the centre of rotation of the angle scale so that one of the two slits
is centred, and use the cover plate to cover the other slit. Position the transmitter on the
angle scale at 200 mm and the receiver on the meter rule at approximately 500 mm (see
Fig. 4). Switch the microwave transmitter on by connecting the control unit to the mains
power supply. Turn the meter rule by 45° (Fig. 5).
Fig. 5: Diffraction through a slit
Remove the double-slit from the beam path and, while doing so, observe the reaction of
the voltmeter. Note down your observation.
Measure also the distance d between the double-slit and meter rule and the width of slit b
by way of the calliper gauge or use the values that are given in the evaluation section.
Second experiment: Diffraction on an obstacle
Connect the microwave transmitter and probe to their associated sockets of the control
unit. Connect the multi-range meter to the voltmeter output of the control unit and select
the 10 V measuring range (direct voltage). Set the amplitude controller to maximum. The
loudspeaker and internal or external modulation are not required for this part of the
experiment.
Fasten the probe to the support rod in the barrel base by way of the boss head. Install the
cover plate in the centre of rotation of the angle scale and position the probe approximately
12 cm behind the plate (see Fig. 6). Switch the microwave transmitter on by connecting
the control unit to the mains power supply.
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Diffraction of microwaves
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Fig. 6: Diffraction on an obstacle
Move the probe perpendicularly to the direction of the propagation of the radiation and,
while doing so, observe the reaction of the voltmeter. Note down your observation.
In addition, the internal modulation and the internal loudspeaker of the control unit can be
used in order to demonstrate the intensity variation behind the double-slit.
Evaluation and result
Check whether the condition for far-field approximation is fulfilled.
With the values b = 2.5 cm, d = 50 cm, and λ = 3.158 cm (see the experiment P2460510
"Standing waves in the microwave range"), the Fresnel number F can be calculated as
follows:
2
F=
2
b
(2.5 cm)
=
≈0.039≪1
d⋅λ (50 cm⋅3.158 cm)
This means that the condition for far-field approximation is fulfilled in an approximative
manner.
Interpretation
Interference and diffraction are phenomena that can only be explained by describing light
(here: light in the microwave range) as waves.
During the diffraction through a (single) slit in the first experiment, for example, the
microwaves are diffracted into an angle (or angular range) so that, when the slit is
removed from the beam path, the intensity under the same angle is lower than before.
During the diffraction on an obstacle (second experiment), a limited intensity can be
measured behind the cover plate, although the plate is made of reflecting metal. This
limited intensity is due to the fact the microwaves are diffracted on the edges of the plate
and that elementary waves propagate into the (alleged) shadow space.
These two experiments cannot be explained without consideration of the concept of
diffraction of waves, i.e. they cannot be explained by geometrical projection (casting of
shadow).
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Diffraction of microwaves
(For instance, the diffraction patterns of two complementary objects, e.g. of a slit and an
obstacle of the same width, or of a circular disc and a circular hole of the same diameter,
cannot be distinguished from one another. This fact is known as Babinet's principle and is
true for all diffraction effects.)
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