Answer:
a) the pattern is bright, b) y = 8.25 mm, c) the distance increases with the wavelength increases
Explanation:
This is a team building exercise to perform interference experiments, where the separation of the slits is d = 1 m = 1 10⁻³ m and the distance to the screen L = 1.5 m
Constructive interference occurs when the path difference is equal to an integer number of wavelengths
d sin θ = m λ
a) The center of the two-ray pattern has the same length so the intensity is MAXIMUM, that is, the pattern is bright
b) to find the distance let's use trigonometry
tan θ= y / L
tan θ =sin θ/cos θ= sin θ
because the angles are small
we substitute
y =
let's calculate
y = 10 550 10⁻⁹ 1.5 / 1 10⁻³
y = 8.25 10⁻³ m
c) for this part the incident light must be white or polychrome light
let's find the distance (y) for some colors, in the first order
Violet λ = 400
y = 1 400 10⁻⁹ 1.5 / 1 10⁻³
y = 6 10⁻⁴ m
green λ = 500 nm
y = 1 500 10⁻⁹ 1.5 / 1 10⁻³
y = 7.5 10⁻⁴ m
yellow λ = 600 nm
y = 1 600 10⁻⁹ 1.5 / 1.10⁻³
y = 9 10⁻⁴ m
lam λ = 700 nm
y = 1 700 10⁻⁹ 1.5 / 1. 10⁻³
y = 1.05 10⁻³ m
violet, green, orange, red
the distance increases with the wavelength increases
d) To find the wavelength we must measure the distance y from the center of the slit for various interference orders and using the equation we can find the wavelength of rationality
