Question

A technician wishes to determine the wavelength of the light in a laser beam. To do so, she directs the beam toward a partition with two tiny slits separated by 0.175 mm. An interference pattern appears on a screen that lies 4.95 m from the slit pair. The technician's measurements show that two adjacent bright interference fringes lie 1.60 cm apart on the screen. What is the laser's wavelength (in nm)

Answer 1

λ = 5.656 x 10⁻⁷ m = 565.6 nm

Step-by-step explanation:

Using the formula of fringe spacing from the Young's Double Slit experiment, which is given as follows:

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

where,

λ = wavelength = ?

Δx = fringe spacing = 1.6 cm = 0.016 m

L = Distance between slits and screen = 4.95 m

d = slit separation = 0.175 mm = 0.000175 m

Therefore,

`\lambda = ((0.016\ m)(0.000175\ m))/(4.95\ m)\\\\`

λ = 5.656 x 10⁻⁷ m = 565.6 nm