How to choose and filter for nikon d3100?

Hi
i want to choose and filter for my camera
i'm not sure though when it comes to stops (4, 6, 10)
can you please explain it

Usually 2x, 4x and 8x (1, 2 and 3 stops respectively) just make sure you buy the one that fits.
I carry an 8x and the now discontinued, 'Hoyarex,' square system.

A Neutral Density (and) filter is used to allow either a) a slower shutter speed when you want to blur running water during the middle of the day or b) when you want to use a larger aperture on a sunny day to decrease your depth of field.
Deciding how many stops of light transmission decrease you need is all but impossible to determine without having a chart of some sort. The following is based on the legacy "Sunny 16 Rule" which states: "On a sunny day, set your aperture to f16 and your shutter speed to 1/ISO." So if its sunny and you're using ISO 100 here is what a "Sunny 16" exposure chart would look like:
f512 @ 15 seconds -10 stops
f360 @ 8 seconds -9 stops
f256 @ 4 seconds -8 stops
f180 @ 2 seconds -7 stops
f128 @ 1 second -6 stops
f90 @ 1/3 second* -5 stops
f64 @ 1/6 second* -4 stops
f45 @ 1/12 second* -3 stops
f32 @ 1/25 second -2 stops
f22 @ 1/50 second -1 stop
f16 @ 1/100 second "Sunny 16"
* Approximate shutter speeds. For our purposes they are adequate. An electronically controlled "stepless" shutter may set a truer shutter speed.
NOTE: If, by chance, you have a lens that stops down to f22 or f32 and you use that minimum aperture you'll need a 2 stop less powerful and filter to achieve the same shutter speeds. Or, to make things simple just use f16.
As you can easily see from the Chart a -10 stop and filter will allow you a 15 second exposure at ISO 100 on a sunny day.
In my opinion there are a couple of problems associated with using regular and filters.
First, if you need maximum flexibility then you'll need more than one and filter. Buying 3 or 4 quality and filters can get expensive rather quickly.
Second, while its quite feasible to "stack" say, a -2 stop and -6 stop to give you a -8 stop decrease in light transmission, the possibly of vignetting when using a wide angle lens may become a problem. Removing the resultant dark corners on your images using an editing program requires "cropping" away part of your image.
So, although admittedly more expensive, I suggest looking at a variable and filter. You can find a comprehensive list of different brands and sizes at B&H - http://www.bhphotovideo.com/...ovideo.com
So instead of having 3 or 4 filters rattling around in your camera bag you'll only have 1 and it will do the job of those 3 or 4.
This tutorial will help you:
http://www.cambridgeincolour.com/...ilters.htm
- ND4 Neutral Density, CPL Lens Filter, UV Lens Filter and Flower Lens Hood?
- How to choose neutral density filter?
- UV filter vs polarisation filter?
- How to remove a uv filter from a dslr without breaking the filter or the lens?
- I want to buy a professional camera and I have to choose from Cannon and Nikon?