Calculate Wavelength Three Different Ways

[Dag]

Homework Statement

The angle to eighth maximum is 1.12. θ_m=1.12
The distance from the slits to the screen is 3.02m. L=3.02m
The distance between the slits is 0.00025m. d=0.00025m
The distance from the first minimum to the fifth minimum is 0.095cm. 0.0295/4=Δx=0.007375m
λ=?

Homework Equations

λ=dΔx/L
λ=dsinθ_m/m
λ=dx_n/L(n-1/2)
λ=dx_m/Lm
λ=dsinθ_n/L(n-1/2)

The Attempt at a Solution

So, I have to calculate the wavelength three different ways, and so far I've managed to find two. The two equations I've used to calculate the wavelength are λ=dsinθ_m/m and λ=dΔx/L. I just need to find another equation to calculate the wavelength. I wanted to use the equation λ=dx_n/L(n-1/2) or the equation λ=dx_m/Lm, but I don't know how to calculate x_n or x_m. So basically, I just need to find another equation to calculate the wavelength and so far, I've been wanting to know how to calculate x_n or x_m. I think I may need to use the equation x_n=λL/2d to calculate x, but I don't have λ, so I can't calculate it that way. Any hints would be much appreciated!

 

[mfb]

I don't see a fundamentally new way - you have two different measurements, both lead to a determination of the wavelength, done. You could calculate the position of the 8th maximum at the screen and then use formulas for the distances instead of the angle, but that would be a more complicated way to repeat the first method.
Or try to fix the errors introduced in the second method where you assume the maxima all have the same distance between them.