How Can You Calculate the Wavelength in a Double Slit Experiment?

[quicksilver123]

Homework Statement

The following data was obtained via the double slit experiment:

angle to the eighth maximum = 1.12 degrees
distance from slits to screen = 302cm = 3.02m
distance from first to fifth mimum = 2.95cm
distance between slits = 0.00025m

find the wavelength.

Homework Equations

supposed to use this equation to find wavelength:

x_n/L=(n-0.5)($\lambda$/d)
or
x_m/L=(m)($\lambda$/d)

The Attempt at a Solution

problem is, there's no given value for x_m or x_n

how can i get this value?

(oh, and i specifically have to use the equation listed above)

 

[Ibix]

$x_m$ is the distance off axis of the mth maximum, numbering the central bright spot as $m=0$. You can immediately write the distance between the Mth and mth maxima as $x_M-x_m=(M-m)L\lambda/d$. A little manipulation gets you $\lambda=d (x_M-x_m)/L (M-m)$. You provided the distance between the M=5 and m=1 maxima. Plugging that and your other data in gets you $\lambda=610$nm.

You also gave the angle to the 8th maximum, which tells us that the distance from the axis to the 8th maximum is 3.02 sin(1.12)=0.059m. Plugging that in with M=8, m=0 also yields 610nm.