Q. 184.5( 8 Votes )
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 :
Fresnel’s distance is given by the relation, Zp = a2 / λ
Where,
λ is the wavelength of the radio waves
Zp is the Fresnel distance, which shows that on distance smaller than this, the spreading due to diffraction smaller compared to the size of the beam.
If we want to prevent diffraction of the radio waves , According to the validity of ray optics, the distance of the middle should be less than The size of aperture “a” = 50 m
Z= 20 km = d/2 = 2 × 104 m
Aperture can be taken as:
a = 50 m
The longest wavelength of radio waves which can be sent without any hindrance due to diffraction effect,
λ = a2 / Zp
⇒ 
⇒ λ = 1250 × 10 - 4 m = 12.5 cm
Therefore, the longest wavelength of the radio waves is 12.5 cm
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PREVIOUSAnswer the following question:Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?NEXTA parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.
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