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?

Solution

Distance between the two towers = 40 km
Size of aperture, $a = 50 m$
Distance of aperture from tower, $Z_{f}$

Fresnel distance is the half of the distance between the towers.

i.e., z_f $= \frac{40}{2} = 20 km = 20 \times 10^{3} m .$
Therefore, now using the formula,

Fresnel distance, $Z_{F} = \frac{a^{2}}{λ}$

we have, $λ = \frac{a^{2}}{Z_{F}} = \frac{(50)^{2}}{20 \times 10^{3}}$

$λ = 125 \times 10^{- 3} m = 12.5 cm .$

This is the required longest wavelength of radio waves, which can be sent in between the towers without considerable diffraction effects.

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Wave Optics

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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Wave Optics

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?

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases: Light diverging from a point source.

What is the shape of the wavefront in each of the following cases: Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What is the shape of the wavefront in each of the following cases:
Light diverging from a point source.

What is the shape of the wavefront in each of the following cases:
Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.