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NCERT Class XII Chapter
Wave Optics
Questions With Solutions

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Question : 18
Total: 21
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?
Solution:  

For diffraction of radiowaves not to occur the distance of middle hill should be less than fresnel distance for a slit width ‘a’ of 50 m.
DF =
a2
λ
Distance between one of the towers and the hill halfway in between
=
40
2
 km = 20000 m = 20 × 103 m
Longest wavelength of radiowave which can be sent without appreciable diffraction effect
λ =
a2
DF
 =
50×50
20×103
 = 12.5 cm
Thus wavelength of radio waves longer than 12.5 cm will bend due to the hill in the middle of towers.
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