Question

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.03 mm apart and position your screen 3.19 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 641 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe

Answer 1

Δx = distance between central bright fringe and first bright fringe = 19.85 x 10⁻⁴ m = 1.985 mm

distance between central bright fringe and second dark fringe = 2.978 mm

Step-by-step explanation:

We have the following data:

λ = wavelength of light = 641 nm = 6.41 x 10⁷ m

L = Distance of Screen from slits = 3.19 m

d = slit separation = 1.03 mm = 1.03 x 10⁻³ m

Δx = distance between consecutive bright fringes = fringe spacing = ?

Using formula:

`\Delta x = (\lambda L)/(d)\\\\\Delta x = ((6.41\ x\ 10^(-7)\ m)(3.19\ m))/(1.03\ x\ 10^(-3)\ m)`

Δx = distance between central bright fringe and first bright fringe = 19.85 x 10⁻⁴ m = 1.985 mm

distance between central bright fringe and second dark fringe = 1.5Δx

distance between central bright fringe and second dark fringe = (1.5)(1.985 mm)

distance between central bright fringe and second dark fringe = 2.978 mm