18.1.4 Interference of Microwaves

Microwaves are electromagnetic waves with wavelengths typically in the range of 1 cm to 30 cm. Because their wavelengths are on the centimetre scale — far larger than visible light — interference patterns produced by microwaves are much easier to measure and demonstrate in a laboratory or lecture hall.

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Experimental Setup

A typical microwave two-source interference experiment uses the following components:

1. A single microwave transmitter — acts as the primary source.
2. A metal barrier with two slits — the single transmitter illuminates both slits, so the two slits act as coherent secondary sources (same frequency, constant phase difference).
3. A microwave receiver (probe) — connected to a galvanometer or loudspeaker, moved along a line parallel to the barrier to detect signal strength.

As the receiver is moved across the interference region, it detects alternating maxima (loud signal / large deflection) and minima (weak or zero signal), confirming the wave nature of microwaves.

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Conditions for a Stable Interference Pattern

For two-source interference fringes to be observed, the sources must be:

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Constructive and Destructive Interference

Let $\Delta p$ be the path difference from the two slits to a point P.

Constructive interference (maximum): $\Delta p=n\lambda ,n=0,1,2,3,\dots$

The waves arrive in phase; amplitudes add up to give a strong signal.

Destructive interference (minimum): $\Delta p=\left(n+\frac{1}{2}\right)\lambda ,n=0,1,2,\dots$

The waves arrive out of phase (crest meets trough); amplitudes cancel to give a weak or zero signal.

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The Double-Slit Formula

For a double-slit (or two-slit) setup where the screen/receiver is far from the slits (far-field approximation):

$\Delta y=\frac{\lambda L}{d}$

Where:

• $\Delta y$ = fringe spacing (distance between adjacent maxima or minima)
• $\lambda$ = wavelength of the microwaves
• $L$ = distance from the slits to the receiver/screen
• $d$ = separation between the two slits

Effect of changing variables:

Worked Example

Two microwave slits are separated by $d=5.0\text{ cm}$. The receiver is placed $L=1.0\text{ m}$ from the slits. The microwave wavelength is $\lambda =3.0\text{ cm}$.

$\Delta y=\frac{\lambda L}{d}=\frac{0.030\times 1.0}{0.050}=0.60\text{ m}$

The fringes are spaced 60 cm apart — easily measurable with a handheld probe.

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Why Microwaves Are Ideal for Demonstrating Interference

• Their centimetre-scale wavelengths produce fringe spacings of tens of centimetres, detectable with simple equipment.
• A single transmitter + two-slit barrier easily creates coherent sources.
• The receiver gives a direct, quantitative reading of intensity at each point.
• No darkroom or special optics are needed, unlike light interference experiments.