Question

We're doing a classic experiment in lhysics lab on measuring the wavelength of a laser using a GEPE difraction grating with 4 slits per mm, where we measure the X values between N=0, and N=1,2,3,... in order to graph the values and calculate a wavelength.

Given that my group set the grating to 304.8cm away from the wall, 10ft, we only had a tape measure... and measured the following x values for each value of N, could someone derive the math for this experiment, and show me how to graph/calculate the wavelength given these values?

N Order	X in CM
1	0.78
2	1.6
3	2.32
4	3.11
5	3.90
6	4.71
7	5.43
8	6.15

I understand the methodology that uses a changing distance, L, from the wall, and uses the Xavg from N=-1 to N=1, but I don't understand how to use this method. I know that they're supposed ot be similiar, buut I just don't understand what the derivation is supposed to look like, or what is plotted against what; so I'm just looking for a full walk through so i can do the other experiments myself, thanks.

Answer 1

i will give you a brief explaination and description of the theory and the formula used to find out the wavelength.

when the laser light of wavelength passes through the diffraction grating, a regular pattern of intensity maxima and minima is seen on the screen. the location of the m^th maxima is given by

          where m=1,2,3.....

here m is the order of the maxima. D is the grating constant or the distance between slits. is the angular displacement of the m^th order maxima from the center of the pattern(the zeroth order maxima which sees normal incidence).

the diagram above shows a schematic diagram of the eperiment setup.

in the experiment we record the distance x_m for different distict orders.(which you have tabulated)

the distance of the screen from the grating is fixed and in your case , L= 304.8cm

now from the diagram it can be easily deduced by basic trigonometry that

so,

we can plug this back in the expression for maxima to get

thats how we get the wavelength.

so as the experimental procedure. you record and tablulate the values of x_m and for each m^th order that you can observe and calculate the wavelength for each m. the wavelength should come out to be the same.

hope this helps