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# Make your own Laser spectrometer !

#### Cyparagon

##### 0
What you need:

Meter stick or Tape measure (metric preferred)
Diffraction grating with known line density*
Calculator
Laser

*If you don't know the line density of your grating, you can find it within ~.5% later on if you have a known stable wavelength (like green).

The concept of diffraction is based on the wave nature of light. Waves interfere to create new wave patterns. Here's a brief overview.

The distance between the waves (lineAC) is the wave length. Basic geometry will show that the two θ shown above are equal. Trig shows us:

sinθ = (lineAC)/(lineAB)
sinθ = λ/d
λ = dsinθ

But since the angle is difficult to measure directly, we will use the projection of the pattern and trig.

tanθ = S/L
θ = arctan(S/L)

So what does all this mean? It means if we have the distance between the grating slits, the distance to the screen, and the distance between diffraction orders, we can find the wavelength!

λ = dsin(arctan(S/L))

"How important are units?" This equation only works if all the units agree, so best to convert everything to meters. That means your wavelength will show up as something like 0.000000658. Don't panic, this equals 658 * 10^-9. Recall that the SI prefix for 10^-9 is nano

"But Cy, my grating says 1000 lines/mm! What does that mean?" 1000 lines/mm is 1000000 lines/m. If we take the inverse, we have .000001 m/line (1µm spacing)

"And what if I don't know the line spacing?" You can find it, but you need a known stable wavelength (Pretty much anything that isn't a laser diode such as DPSS or gas lasers). Set everything up and take the two measurements. You have all variables except the line spacing. We can rearrange the equation to get d = λ / sin(arctan(S/L))

"Cool! So how accurate is this in practice?" Well it depends on how accurate your measurements and alignments are. Even if you do everything perfectly, there is still the variation in the grating itself. For best results, have the laser perfectly perpendicular to both the screen and grating, and have the screen far away - at least a meter. When I set this up, I found it was accurate to ± 4nm compared to my calibrated CCD spectrometer, but it was done on the kitchen floor with film grating and a floppy tape measure. Your results will vary. I don't want to see anyone claiming their laser is 657.23981247293847 nm like some people like to do with divergence. Your ruler is not accurate enough to have that many significant figures At least round to the nearest nm. It is also advisable to indicate an error margin, since it may be rather large. But if nothing else, it's a fun experiment

Let me know what you think. Post your results! :beer:

edit: rhd made an applet if you don't have a calculator: http://rohanhill.com/tools/FindWavelength/

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#### Kevlar

##### 0
Cy, this awesome! I haven't had to use trig in 20 years though...

This needs a sticky! :beer:

#### Cyparagon

##### 0
The proof itself might be difficult to understand if your trig is rusty, but as long as you can find the buttons on a calculator, you don't need to understand what they do

#### Elektrotechniker

##### 0
+1 for you sir. I moved to my parents house for the holidays and I forgot to bring laser stuff. Will try to make this experiment when I get back Seems very fascinating!

#### jcranmer

##### 0
Wow. My head huts. I love science, but hate math!

#### Tonga

##### 0
Thanks man! +rep.

#### Johnyz

##### 0
Now, what precision in measuring S do I need to get an accurate result? I'm thinking of a digital spectrometer with an array of photodiodes to do the trick, AVR Cam to measure would be pretty expensive...

#### Cyparagon

##### 0
Garbage in, garbage out. Millimeter should suffice.

##### 0
Thanks for this nice summary of diffraction theory:gj:

I just want to give a warning: savety goggles are a MUST with diffraction gratings, especially with glass gratings. Plus, with goggles you can measure the distance of the spots much more precise, because you avoid the large blooming:yh:

Rep+ for this nice topic!

#### anselm

##### 0
So I tried this, but it doesn't work for me...

I used the grating from a PHR sled.
I used an L of 13 meters.
Here are a couple of Ss:
405nm -> 57.2cm
532nm -> 57cm
635nm -> 56.8cm
660nm -> 56.9cm

The only real differences I can see are likely measurement errors....:thinking:
Not enough precision to get any useful results.

Maybe the grating is not the right one...
Maybe I'm going to try with a CD.

#### Cyparagon

##### 0
Yeah, something's wrong. It's not possible for all wavelengths to have the same angle.

I tried a CD with a measuring tape through my living room. Using 488 for a reference, I calculated the spacing to be ~1.25µm, and the green line to be ~512nm (~2nm off). So even with my half-ass job, it worked okay.

Google tells me the spacing should be 1.6µm, which is a little strange. I tried again with a factory-stamped CD and got a slightly larger spacing of ~1.3µm.

I'm working with mister rhd who can hopefully develop a web-app to make this more simple.

#### laser_freak

##### 0
For a web-app, it may be simpler to have the user place the diffraction grating immediately in front of the camera lens, instead of in front of the laser. The distance between the orders can be measured in pixels, and the wavelength per pixel can be calculated*. This is much simpler, for a large distance between the grating and the measuring surface is no longer needed for accuracy. The downside is that the accuracy is directly dependent on the resolution of the camera and the focal length of the lens. I use this method all the time for spectroscopy.

If the diffraction grating's line density and focal length of the lens are known, the wavelength per pixel can be calculated without a reference laser.

*This number would change with the focal length of the camera, so either a fixed focus would be needed, or a reference laser would need to be used in every image.

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#### Roy G. Biv

##### 0
If the diffraction grating's line density and focal length of the lens are known, the wavelength per pixel can be calculated without a reference laser.

How do you calculate this?

#### RobisonCarusolie

##### 0
Thanks to the Almighty for you, if I may, Cyparagon. Indeed I hope to look at blood samples for analysis.
I speak in liue of part time jobs only, slow stickers on vehickes, P.E.A.R. projects future consciousn "sin" detection unit, and saying such to others...oh yeah, THE (flysing saucer Box- jt schiffer jr.) AGAIN, Thanks sense this is life saving if you understand the need for blood analysis.

#### BShanahan14rulz

##### 0
:bowdown::bowdown::bowdown::bowdown:
I agree! Vehicular blood analysis ventricle spectroscope A.P.P.L.E project. Instead of full time jobs, to shine laser at for to detection of "evil" in blood.