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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1) 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. www.phywe.com P2460810 PHYWE Systeme GmbH & Co. KG © All rights reserved 1 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. 2 PHYWE Systeme GmbH & Co. KG © All rights reserved P2460810 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 www.phywe.com P2460810 PHYWE Systeme GmbH & Co. KG © All rights reserved 3 DEP 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. 4 PHYWE Systeme GmbH & Co. KG © All rights reserved P2460810 Diffraction of microwaves DEP 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). www.phywe.com P2460810 PHYWE Systeme GmbH & Co. KG © All rights reserved 5 DEP 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.) 6 PHYWE Systeme GmbH & Co. KG © All rights reserved P2460810