Young Double Slit Experiment (Determine wavelength of light source)

HarleyM

1. The problem statement, all variables and given/known data
Upon using Thomas Young's double slit experiment to obtain measurements, the following data was obtained. Use this data to determine the wavelength of light being used to create the interference pattern. DO this in 3 different ways!

• The Angle to the Eighth maximum is 1.12 deg.
• The distance from the slits to the screen is 3.02 m
• The distance from the first minimum to the fifth minimum is 2.95 cm
• The distance between the slits is 0.00025 m

2. Relevant equations
sin∅_n=(n-1/2)λ/d
sin∅_m=mλ/d
Δx=Lλ/d
X_n/L=(n-1/2)λ/d
X_m/L=mλ/d
3. The attempt at a solution
sin∅_n=(n-1/2)λ/d
λ=(sin1.12)(0.00025)/(7.5)
λ=651 nm


The distance from the first minimum to the fifth minimum is 2.95 cm .. therefore
4Δx=2.95 cm
Δx=0.0074 m ( i converted it)

Im unsure about 4 x if anyone can shed any light on that that would be cool


Δx=Lλ/d
λ=Δxd/L
λ=(0.0074) (0.00025)/ (3.02)
λ= 612 nm

as for this one I dont know if I should use the X_m or X_n equation..I used

X_m/L=mλ/d

(0.0295)/3.02=4λ/(0.00025)
λ= 610 nm

Number seems plausible but it also does when I use the X_n equation

thanks for any help in advance

technician

Using Sinθ = 8λ/d for the 8th max I got λ = 6.1 x 10^-7m
Using 4x for the separation of 5 minima then using x = λL/d I got λ = 6.1 x 10^-7m

HarleyM

since its a max shouldn't you use sin∅=(n-1/2)λ/d?

technician

For a max the path difference from the slits must be a whole number of wavelengths.
For the 8th max the path diff = 8 wavelengths.
For minima the path diff must be an odd number of half wavelengths (n+1/2) but the SEPARATION of max and min is given by increases in path diff of whole numbers of wavelengths.
Hope that sounds OK