# Interference of light, emission spectroscopy prac. report

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1. Aug 7, 2017

### cumlord

Ok, so I've got a practical report due tomorrow and I just wanted to clarify a few things. A bit of background knowledge first. The practical involved taking angular measurements for the emission lines of the Mercury spectrum using the apparatus, a spectrometer and a Mercury spectral tube, pictured here: http://imgur.com/Xkp8J01

We were supposed to use these recorded angular measurements to calculate the wavelengths of light corresponding to these emission lines using the diffraction grating formula dsin(theta)=m(lambda) where m is the order of the spectrum, and d is the distance between the slits (which was 1693nm). The results we collected, and the subsequently calculated wavelength values, are pictured here for the lines to the right of the central maximum: http://imgur.com/1ituoqq

and here for those to the left of the central maximum (Red-1 was treated as the maxima used throughout calculations since it was of the strongest intensity. The rest are assumed to be ghost lines): http://imgur.com/Xw0RzEa

As you can see, the angular measurements differ on either side of the central maximum, and so, where applicable, I added the angle recorded for a maximum within a certain order spectrum on one side of the central maximum to the angle recorded for the other side for the same emission line, and divided the result by two (Here's an image that shows my workings: http://imgur.com/hr5cBDo). For the emission lines that appeared in numerous orders, the results from the above process were averaged (Again, my working for this: http://imgur.com/eoKOlGD).

My questions are as follows:

1.) Why is the angle measured for a certain emission line in the first order spectrum seen as more accurate than the angle measured for the same emission line in the second or third order spectrum? Is it because of the faintness of the emission lines in greater order spectra, or is it because they involve greater angular measurements which leaves a greater margin of error?

2.) The theoretical Mercury spectrum that I am using is pictured here: http://imgur.com/Czr6wmD As you can probably tell, the wavelength values for the orange and aqua emission lines differ significantly from the values we obtained. Is it perhaps because the spectral tube we used contained a different isotope of Mercury or perhaps some impurities? I've read that Mercury lamps usually have Phosphor coatings on the outer bulb. Could some of the unexplained observed emission lines be due this Phosphor?

3.) Can you suggest any errors that may apply to this practical? I've thought of 2 systematic and 2 random but I feel I need more.

I understand a lot of people are busy so any help would be much appreciated. If you require any other information to answer the questions please ask. Also, if you spot any errors in my results, calculations, or anywhere else please let me know.

2. Aug 7, 2017

### BvU

Hello cum,

Bit of a hurry eh ?
I think you did some pretty good measuring work: my compliments. Working it out the way you do is reasonable, but there is some room for improvement. In particular: the 1693 nm is a common factor for all observations, hence a systematic error source -- it does not average out. As I expect you already thought (what are your 2 systematic and your 2 random errors ?).

1. Says who ? I can imagine the small angle approximation $d \tan\theta = m\lambda$ (with $\tan\theta = y/L$ where y is a perpendicular distance on a screen that is L away) introduces a small error for higher orders, but your instrument measures actual angles.