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Unformatted text preview: 23. (a) The ﬁrst minimum in the diﬀraction pattern is at an angular position θ, measured from the center
of the pattern, such that sin θ = 1.22λ/d, where λ is the wavelength and d is the diameter of the
antenna. If f is the frequency, then the wavelength is
λ= c
3.00 × 108 m/s
=
= 1.36 × 10−3 m .
f
220 × 109 Hz Thus
θ = sin−1 1.22λ
d = sin−1 1.22(1.36 × 10−3 m)
55.0 × 10−2 m = 3.02 × 10−3 rad . The angular width of the central maximum is twice this, or 6.04 × 10−3 rad (0.346◦ ).
(b) Now λ = 1.6 cm and d = 2.3 m, so
θ = sin−1 1.22(1.6 × 10−2 m)
2.3 m = 8.5 × 10−3 rad . The angular width of the central maximum is 1.7 × 10−2 rad (0.97◦ ). ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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