Question

Parallel rays of monochromatic light with wavelength 583 nm illuminate two identical slits and produce an interference pattern on a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm. If the intensity at the center of the central maximum is 5.00×10^−4W/m^2. What is the intensity at a point on the screen that is 0.900 mm from the center of the central maximum?

Answer 1

I = 2.18 10⁻⁴ W / m²

Step-by-step explanation:

The two-slit interference pattern is described by the expression for constructive interference.

d sin θ = m λ

If we also want to know the distribution of intensities we must perform the su of the electric field of the two waves, and find the intensity as the square of the velvet field, obtaining the expression

I = I_max cos² ((π d /λ L) y)

where d is the separation of the slits, λ the wavelength, L the distance to the screen e and the separation of the interference line with respect to the central maximum

let's reduce the magnitudes to the SI system

λ = 583 nm = 583 10⁻⁹ m

L = 75.0 cm = 75.0 10⁻² m

d = 0.640 mm = 0.640 10⁻³ m

y = 0.900 mm = 0.900 10⁻³ m

let's calculate the intensity of this line

I = 5 10⁻⁴ cos² ((π 0.640 10⁻³ /583 10⁻⁹ 0.75 10⁻²) 0.900 10⁻³)

I = 5 10⁻⁴ cos2 (413.84)

I = 5 10⁻⁴ 0.435

I = 2.18 10⁻⁴ W / m²