Verified answer

Bonjour,

A)

1) pour D >> a, on a : λ/a = L/2D

soit : λ/L = a/2D

donc constante

⇒ λ₂ = λ₁ x L₂/L₁ = 450 x 3/2 = 675 nm

2)

D = aL/2λ ⇒ D = 280.10⁻⁹ x 2.10⁻²/2 x 450.10⁻⁹ = 280/450 ≈ 0,62 m

B) 1)

sin(i) = nsin(i') et sin(r) = nsin(r')

⇒ sin(r') = sin(r) x sin(i')/sin(i) = sin(r)/K    avec K = sin(i)/sin(i')           (1)

Or A = r + r' ⇒ sin(r') = sin(A - r) = sin(A)cos(r) - cos(A)sin(r)                (2)

(1) et (2) ⇒ sin(r)/K = sin(A)cos(r) - cos(A)sin(r)

⇔ sin(r) x [1/K + cos(A)] = sin(A)cos(r)

⇔ sin(r)/cos(r) = sin(A)/[1/K + cos(A)]

soit tan(r) = sin(A)/{1/K + cos(A)]

2.1) D = i - r + i' - r' = i + i' - A ⇒ i = D + A - i' = 10 + 30 - 20 = 20°

⇒ 1/K = sin(i')/sin(i) = sin(20)/sin(20) = 1

⇒ tan(r) = sin(30)/[1 + cos(30)] = (1/2)/[1 + √(3)/2] = 1/(2 + √(3))          (≈0,267949...)

⇒ r = arctan[1/(2 + √(3)) = 15°

2.2) n = K = 1 !!