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Ref :
223 008
The computerised study of the denominator Φ(θ) of δ by mans of ACTILAB yields its
variations in the experimental conditions.
θ varies at most in the range from -60° to +60° (from -π/3 to +π/3)
For the selected values of a and D, the representative curve of Φ(θ) versus θ gives the
following graph:
For the value 2D=30 cm, the relative difference (Φ(θ)-2D)/2D is 0.27/30 or 0.9% maximum at
the angular abscissa θ=0°. The relative difference drops to about 0.21/30 or 0.7% for θ=+π/6
or -π/6, and it reached 0.6/30 or 0.2% for θ=+π/3 or -π/3.
Therefore, 2D can be substituted for Φ(θ).
Then the expression of the course difference is:
For the peaks, we express δ=
Since
For a=4 cm, we have
Since -π/3
-0.866
The possible values of k for the amplitude peaks are:
k=-4, k=-3, k=-2, k=-1, k=0. k=1, k=2, k=3 and k=4.
ENGLISH
Approximations
Number of peaks
λ
is constant for a given value of a,
a
λ
, 0
=
a
4
≤
≤
θ
+π/3, we have -0.866
≤
≤
, 0
21
k .
+0.866 or else -4.12
δ
θ
≈
a
sin(
)
λ
θ
θ
≈
k
.
a
sin(
)
sin(
or
θ
sin(
)
is an integral multiple of
84
=
sin(
, 0
21
and we have
θ
≤
≤
sin(
)
+0.866, or
≤ k
≤
+4.12
49
λ
k
.
≈
)
(λ=0.84 cm).
a
λ
.
a
θ
)
=0.21.k.
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