Question

The Voyager 1 space probe radio transmitter had a total power output of only 40 W. The transmissions were made at either 2.3 GHz or 2.4 GHz, using an antenna with a diameter of 3.7 m.

Knowing that the diameter of the aperture limits the angular spread of the beam due to the Reyleigh criterion, What was the diameter of the central maximum of the beam at the earth when voyager reached Pluto?

Answer 1

Solution :

In question given that , Antenna diametre is ,

And average value of Wavelength is ,

=(2.3+2.4)/2

=2.35 GHz

or ( let the transmitted wave is travel with velocity c)

or

  

The beam produced by this microwave transmission antenna will spread out at  a minimum angle due to diffraction   ( called Rayeligh cretreon)

and antenna aperture is circular with diametre D ,So   for a circular aperture of diameter , the first minimum in the diffraction pattern occurs at  (providing the aperture is large compared with the wavelength of light)

radian

And Graph of intensity of the diffraction pattern for a circular aperture. similar to a single slit, the central maximum is wider and brighter than those to the sides

shown in fig.

So in fig . is the width or a Diametre of central maxima, And its value equals