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 1.03 mm and place your screen 9.25 m from the slits. then you illuminate the slits with your new toy and find on the screen that the tenth bright fringe is 4.72 cm away from the central bright fringe (counted as the zeroth bright fringe). what is your laser\'s wavelength expressed in nanometers?

So for double-slit, the equation is mλ=dsinθ. We are solving for λ. So we are told that our slit spacing is 1.03mm = 1.03*10^-3m = d. We are also given that the screen is 9.25m away from the slit and that the 10th bright fringe is 4.72cm away from the central fringe.

I won't show you how to derive it, but you can always try to prove it.

We know mλ=dsinθ. Since the screen is very far (relative to the wavelength), we can approximate sinθ≈θ and θ≈tanθ.

From the screen tanθ = x/R R: distance from the screen. x: distance from the central fringe. Substituting x/R into sinθ, we get:

λ

Remember, it is at the tenth bright fringe, so m=10
Substituting our known values in, we get:

λ

Solving for λ, we get:

λ=