Answer:
I = 0.56 10⁻⁴ W / m²
Explanation:
Double-slit interference is described by the expression
d sin θ = m λ
if we use trigonometry we can find the angle
tan θ= y / L
how the angles are small
tan θ = sin θ / cos θ = sin θ
sin θ = y / L
we substitute
d y / L = m λ
if we take into account that each slit also produces a diffraction phenomenon, the intensity distribution is the product of the intensity of the slits by the intensity of the diffraction process
I = I₀ cos² (d a) [(sin ba) / ba]²
a = π sin θ /λ
where the separation of the slits and b is the width of the slits
we substitute
I = I₀ [cos (d a)]² [sin ba /ba]²
a = π y / (L λ)
let's reduce the magnitudes to the SI system
λ = 582 nm = 582 10⁻⁹ m
L = 75.0 cm = 75.0 10⁻² m
d = 0.640 mm = 0.640 10⁻³ m
b = 0.434 mm = 0.434 10⁻³ m
Io = 4.40 10⁻⁴ W / m²
let's calculate for y = 0.710 mm = 0.710 10⁻³ m
a = π 0.710 10⁻³ / (75 10⁻² 582 10⁻⁹)
a = 5.11004 10³
I = 4.40 10⁻⁴ [cos (0.640 10⁻³ 5.11004 10³)]² (sin (0.434 10⁻³ 5.11004 10³) / (0.434 10⁻³ 5.11 10³)²
I = 4.40 10⁻⁴ cos² (3.2704) (sin 2.2178 / 2.2178)²
remember that the angles are in radians
I = 4.40 10⁻⁴ 0.9835 (0.79789 / 2.2178)²
I = 4.40 10⁻⁴ 0.9835 0.1294
I = 0.56 10⁻⁴ W / m²
