Two towers on top of two hills are 40 km apart. The line joining them passes 50 m above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the towers without appreciable diffraction effects?

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Solution

Distance between the towers is 40km.
Height of the line joining the hills is $d = 50 m$ .
Thus, the radial spread of the radio waves should not exceed 50 m.
Since the hill is located halfway between the towers, Fresnel’s distance can be obtained.
$Z_{P} = 20 k m$
Aperture is $a = d = 50 m$
Fresnel’s distance is given by the relation,
$Z_{P} = a^{2} / λ = 2 \times 10^{4}$
$λ = a^{2} / Z_{P} = 12.5 c m$

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