# Calculate Wavelength Three Different Ways

1. Feb 27, 2015

### Dag

1. The problem statement, all variables and given/known data
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=?

2. Relevant equations
λ=dΔx/L
λ=dsinθm/m
λ=dxn/L(n-1/2)
λ=dxm/Lm
λ=dsinθn/L(n-1/2)
3. 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=dsinθm/m and λ=dΔx/L. I just need to find another equation to calculate the wavelength. I wanted to use the equation λ=dxn/L(n-1/2) or the equation λ=dxm/Lm, but I don't know how to calculate xn or xm. 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 xn or xm. I think I may need to use the equation xn=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!

2. Feb 27, 2015

### Staff: Mentor

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.