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( 6 months ago )

Fresnel's distance in radio waves

Course Queries Syllabus Queries
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Rukhsar Fatima

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( 6 months ago )

 

I am not able to solve the below question in wave optics of Indian ncert syllabus

Two towers on top of two hills are 40km apart. The line joining them passes 50m 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 ?

The book solves it this way,

The hills will not obstruct the transmitted radio waves,if over the halfway distance (Z¬F) between the hills,the spreading of the signal is limited to the distance(a) of the line of sight from the hills,

Here,Fresnel’s distance Z¬F = 20km = 20 x 103m,a = 50m, Now, Z¬F = a²/λ,λ = 502/20 x 103 = 0.125m.

My concern is in the formulae of Fresnel’s distance Z¬F = a²/λ, Z¬F is the distance between the slit and the screen,a is the size of the aperture, here I am not finding any aperture as above the middle hill the air spreads till infinity,

Z¬F in this case is the distance between the aperture and the screen, Even though m not finding any slit or screen, Zf should be the distance between the middle hill and the third hill but in the book it is between the first hill and the middle hill,

I am not getting what the situation is all about in this question and how to go about solving it, Thanks.

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