Advertisement Remove all ads

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? - Physics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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?

Advertisement Remove all ads


Distance between the towers, = 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:

d = 50 m

Fresnel’s distance is given by the relation,

`Z_p = a^2/lambda`


λ = Wavelength of radio waves

`:. lambda = a^2/Z_p`

`= (50)^2/(2xx10^4) =- 1250 xx 10^(-4) = 0.1250 m = 12.5 cm`

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

Concept: Diffraction - The Validity of Ray Optics
  Is there an error in this question or solution?


NCERT Class 12 Physics Textbook
Chapter 10 Wave Optics
Q 18 | Page 385
Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×