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 1.11 mm and place your screen 8.63 m from the slits. Then, you illuminate the slits with your new toy and find on the screen that the tenth bright fringe is 4.71 cm away from the central bright fringe (counted as the zeroth bright fringe). What is your laser's wavelength lambda expressed in nanometers?

Answer 1

λ = 605.80 nm

Step-by-step explanation:

These double-slit experiments the equation for constructive interference is

d sin θ = m λ

where d is the distance between the slits, λ the wavelength of light and m an integer that determines the order of interference.

In this case, the distance between the slits is d = 1.11 mm = 1.11 10⁻³ m, the distance to the screen is L = 8.63 m, the range number m = 10 and ay = 4.71 cm

Let's use trigonometry to find the angle

tan θ = y / L

as the angles are very small

tan θ = sin θ / cos θ = sin θ

we substitute

sin θ = y / L

we substitute in the first equation

d y / L = m λ

λ = d y / m L

let's calculate

λ = 1.11 10⁻³ 4.71 10⁻²/ (10 8.63)

λ = 6.05805 10⁻⁷ m

let's reduce to nm

λ = 6.05805 10⁻⁷ m (10⁹ nm / 1m)

λ = 605.80 nm