Finding a third method to determine light wavelength

[chef99]

Homework Statement

a) explain why a pattern of bright and dark fringes is visible on a screen when a light is shone through a double slit.
b) Use this data to determine the wavelength of light being used to create the interference pattern. Do this three different ways.
-The angle to the eighth maximum is 1.12º
-The distance from the first minimum to the fifth minimum is 2.95 cm
-The distance between the slits is 0.00025cm

Homework Equations

mλ =dsinθ_m
Δx = Lλ / d

The Attempt at a Solution

First method
[/B]
mλ =dsinθ_m

λ = dsinθ₈ / m

λ = (2.5x10^-4m)(sin1.12deg) / 8

λ = 6.108 x10^-7m

λ = 611nm

Second method

Δx = Lλ / d

λ = dΔx / L

λ = (2.5 x10^-4m)(7.375 x10^-3) / (3.02)

λ = 6.105 x10^-7m

λ = 611nm

I am confident these two are correct, as they both give a very similar result. The slight differences are likely due to rounding/ calculating errors within an acceptable range.
My issue is I can't figure out the third method to use, the equation I believe must be used is (n-1/2) λ = dx_n / L (or for the maximum mλ = dx_m / L) however I can't figure out how to determine the value for x_n / x_m with the data that is given in the question. The only other equations that were taught in this lesson were
| P_nS₁ - P_nS₂ | = mλ and the version for using minimum values.
This equation is obviouly not usable since the values of P_nS₁ and P_nS₂ are not given/determinable with the given data.
Any suggestions on how to determine the value of x_n / x_m, or if I even have the right idea are greatly appreciated.

 

[mfb]

Where did L come from?

You just have two measurements given, that leads to only two completely independent estimates. Everything else will be somewhat similar to one of the others. You can use the distance value and convert it to an angle, or calculate the separation of the main maximum and first minimum based on it, or something silly like that.

 

[chef99]

Where did L come from?

You just have two measurements given, that leads to only two completely independent estimates. Everything else will be somewhat similar to one of the others. You can use the distance value and convert it to an angle, or calculate the separation of the main maximum and first minimum based on it, or something silly like that.

Sorry I forgot to add that the value of L was given:

- The distance from the slits to the screen is 302 cm

 

[chef99]

Where did L come from?

You just have two measurements given, that leads to only two completely independent estimates. Everything else will be somewhat similar to one of the others. You can use the distance value and convert it to an angle, or calculate the separation of the main maximum and first minimum based on it, or something silly like that.

With L = 302cm, I have come up with this possible solution. I'm not sure if this is right at all but it gave me the same answer as the other two (611nm).

using (n-1/2) λ = dxn / L,

Given: Required: λ

L = 302cm
d = 0.00025m = 2.5 x10^-4m
4Δx = 2.95cm; therefore Δx = 2.95cm / 4
Δx = 0.7375cm = 0.007375m
n = 1

(n-1/2) λ = dxn / L

λ = dxn / L (n - 1/2)

λ = (2.5 x10^-4m)(0.007375m) / (3.20m)(1)

λ = 6.105 x10^-7m

λ = 611nmThis answer gives 611nm, same as the other two methods, the part I don't know if I did correctly was using n = 1 in the equation.

 

[mfb]

That works, but I'm not so sure about the "independent". The distance between the central maximum and the first maximum is 1/4 the separation between first and fifth minimum. You just shifted the place where you divide by 4.