I will be going to Paris in 2 weeks for vacation. I just bought a Nikon 10-24mm lens for my 300s. Would I benefit from using a polarizer for this lens while shooting there? I have looked to purchase the Nikon Polarizer.
Polarizing filters are of very limited use for wide angle lenses, since the degree of polarization changes over the wide angle of view. This results in uneven coloring of blue sky. I generally don't use a polarizer for lenses wider than about 35mm with an FX camera which corresponds to a limit of 24mm for a DX camera.
People sometimes use polarizing filters for wide angle lenses to suppress reflections from wet leaves or water surfaces, but I don't think you will encounter any such situation in Paris, particularly at this time of the year.
The predominant effects afforded by a circular polarizer are very difficult to near impossible to duplicate in post processing. These include haze reduction, and glare and reflection control. The polarizer also has the benefit of giving you additional perceived saturation - this can usually be simulated in post. The downsides are they are tricky to use on wide angle lenses and if cranked up all the way they can darken a blue sky to almost black at higher altitudes. There is no reason you can't use one on a 10-24mm, I have, you just need to use it judiciously. Don't use it at the widest settings of the lens (I agree 24mm is about the limit) and check the sky in the viewfinder to make sure you are not creating uneven color in the sky. Try to keep the sun at a ninety degree angle to the shooting plane for maximum effect and control and you should be okay.
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What Ernesto says is correct. A polarizer can be useful on this lens, but you need to be aware of how it can mess up the sky and avoid using it in those situations.
You can't replicate the glare-reducing effect of a polarizer in post, and it would be very difficult to remove a half-polarized sky too.
BTW you don't need a slim polarizer with this lens, although it doesn't hurt, particularly if you might stack an ND on as well (for shooting waterfalls for example). I posted a lens test showing no additional vignetting for any focal length using a B+W (thick) pol. You can probably find it searching the Nikkors forum.