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:
[tex]d \frac{x}{R} =m[/tex]λ
Remember, it is at the tenth bright fringe, so m=10
Substituting our known values in, we get:
[tex](1.03*10^{-3} ) \frac{4.72*10^{-2}}{9.25} = 10 [/tex]λ
Solving for λ, we get:
λ=[tex]5.255783784*10^{-7}m = 525.578nm[/tex]
