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Class 12
Physics
Wave Optics
two towers on top of two hills are 40 km apart th...

Question:
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?

Answer:

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: Z _P = 20 km = 2 × 10 ⁴ m

Aperture can be taken as, a = d = 50 m

Fresnel’s distance is given by the relation, Z_p = a²/λ

Where, λ = Wavelength of radio waves

Therefore, λ = a²/Z_p = (50)² / 2x10⁴ = 1250x10^-4 = 0.1250 m = 12.5 cm

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

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Question:
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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Question: 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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Question:
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?