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, - Physics

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Numerical

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, d = 40 km

Height of the line joining the hills, d = 50 m.

Thus, the radial spread of the radio waves should not exceed 50 km.

Since the hill is located halfway between the towers, Fresnel’s distance can be obtained as:

ZP = 20 km = 2 × 104 m

Aperture can be taken as:

a = d = 50 m

Fresnel’s distance is given by the relation,

`"Z"_"p" = "a"^2/lambda`

Where,

λ = Wavelength of radio waves

∴ `lambda = "a"^2/("Z"_"p")`

= `(50)^2/(2 xx 10^4)`

= −1250 × 10−4

= 0.1250 m

= 12.5 cm

Therefore, the wavelength of the radio waves is 12.5 cm.

Concept: Diffraction of Light - The Validity of Ray Optics
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Chapter 10: Wave Optics - Exercise [Page 385]

APPEARS IN

NCERT Physics Class 12
Chapter 10 Wave Optics
Exercise | Q 10.18 | Page 385
NCERT Physics Class 12
Chapter 10 Wave Optics
Exercise | Q 18 | Page 385
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