If I stacked a Vivitar ND8 and ND2 filter, would they function as well as an ND16? Would this work for solar photography, or would a piece of welding glass be better?
Edit: I also have an ND4 if that would be useful.
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The numbers in the ND filters are powers of two (of light reduction), so stacking an ND8 with an ND2 gives an ND10. If you add the ND4, you get ND14, which is normally enough to photograph directly into the sun.
However, depending on the filters, they do not filter out infrared or ultraviolet, so the sun might still fry your sensor (or your eye, if you look into the viewfinder).
Filters specifically made for sun viewing will have their filtering capacity extending sufficiently into IR and UV ranges (unless they are cheapo fakes...).
To your question, the difference is that you will have a multitude of glass surfaces, that will deteriorate the picture quality. ND filters are often poorly coated, and having six surfaces of poorly coating results in quite some reflections, etc. still, this is probably not too big an issue, unless you are trying to do high-end photography, for billboards or large prints. For computer screen viewing, or 6x8 prints, that should not be an issue.
You can stack filters to your heart's content but --- Good filters are optical flats (both sides are parallel). When you stack each filter adds two polished surfaces. Some light is reflected away, maybe 1% if coated and up to 4% if not coated. Seems OK for ND's but -- all added surfaces except the first, reflect and contribute stray light that commingles with the imaging forming rays. These find their way to film or imaging chip. The result is added flare. Flare is devastating as it robs the image of contrast. OK to stack just be alert as to what can happen.
The previous answers address the flaws when multiple filters are used and the problems with colours (They are not as neutral as one might assume) and suitability for sun observations.
I just want to add a bit more information about the numbers and the maths behind:
There are various incosistant naming schemes around when it comes to ND filters.
Depending on the scheme in use you have to do different calculations.
Scheme 1: (prolongation factor given)
ND2, sometimes also labeled NDx2 means a factor of 2 (1 F-stop), ND8 means factor 8 (3 F-stops). If this scheme is used, you have to multiply the numbers given to get the resulting prolongation factor: ND8+ND2 => 8*2 (3+1 F-stops) => 16 (4 F-stops).
The Vivitar filters mentioned seem to use this scheme. For some reason Vivitar states that the ND8 results in 4 F-stops. This does not match any of the calculation schemes I know.
This scheme is used on Rollei, Cokin or Hoya filters.
Scheme 2: (F-Stops given)
The ND numbers are the F-stops gained by the filter. A ND2 gives 2 F-stops, resulting in 4 times longer exposure. Stacking filters means adding the numbers. ND8 + ND2 = ND10 = 10 F-stops.
I currently don't know any manufacturor using this scheme. I think I saw it once but don't remember the brand. Maybe it's not used anywhere anymore.
Scheme 3: (density given)
The neutral density is the decimal logarithm of the prolongation factor. ND1 means 10 times longer exposure. ND0.3 => 1 stop; ND0.6 => 2 stops; ND 3.0 => 1000* (~10 stops) Combining filters requires adding up the density values. ND0.3+ND0.6 => ND0.9 (3 stops).
This is used for B+W, Lee, Hitech and Haida filters.
As Vivitar seems to use the first scheme, the 2 filters would result in 4 F-stops.