Question

You perform a double‑slit experiment in order to measure the wavelength of the new laser that you received for your birthday. You set your slit spacing at 1.09 mm and place your screen 8.61 m from the slits. Then, you illuminate the slits with your new toy and find on the screen that the tenth bright fringe is 4.53 cm away from the central bright fringe (counted as the zeroth bright fringe). What is your laser's wavelength ???? expressed in nanometers?

Answer 1

λ = 5.734 x 10⁻⁷ m = 573.4 nm

Step-by-step explanation:

The formula of the Young's Double Slit experiment is given as follows:

`\Delta x = (\lambda L)/(d)\\\\\lambda = (\Delta x d)/(L)`

where,

λ = wavelength = ?

L = distance between screen and slits = 8.61 m

d = slit spacing = 1.09 mm = 0.00109 m

Δx = distance between consecutive bright fringes =
`(4.53\ cm)/(10)` = 0.00453 m

Therefore,

`\lambda = ((0.00453\ m)(0.00109\ m))/(8.61\ m)`

λ = 5.734 x 10⁻⁷ m = 573.4 nm