Ncert Exercises & Solutions

10.18 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?

Hint: $Z_{p}=\frac{a^{2}}{\lambda }$

Step 1: Find aperture.

Distance between the towers, d = 40 km.
Height of the line pining the hills, d = 50 m.
Aperture, a = d = 50 m.
Step 2: Find Fresnel's distance.
Since the hill Is located halfway between the towers, Fresnel's distance can be
obtained as: $Z_{p} = 20 k m = 2 \times 10^{4} m$
Step 3: Find the longest wavelength of radio waves.
Fresnel’s distance is given by the relation,

$As Z_{p} = \frac{a^{2}}{λ}$

$\begin{array}{l} ∴ λ = \frac{a^{2}}{Z_{p}} \\ = \frac{(50)^{2}}{2 \times 10^{4}} = 1250 \times 10^{- 4} = 0.1250 m. = 12.5 c m. \end{array}$

Therefore, the wavelength of the radio waves is 12.5 cm

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions