I bought some filters a few months ago with a 72mm thread. Now I find myself buying a new lens with a 77mm thread. I have never used step up/down rings before.
What the pro and cons of using an adapter for this as it is only 5mm difference.
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A step-down ring is required to physically mount the 72mm filter on a lens with a 77mm thread. Since this is a step-down adapter rather than a step-up, the field-of-view of the lens may become partially obstructed, causing severe vignetting or even appearing visible at corners of the frame.
Essentially, there is no pro for doing this, only downsides because you are losing part of your image. Even when you crop the blocked-out corners, you have lost resolution and angle-of-view. The same can happen when use the wrong lens hood is used on a lens, even though it may fit the bayonet.
The amount of vignetting that occurs depends on the lens used and the set focal-length in case of the zoom. It could be the case that no vignetting occurs at all if the lens does not need that wide a filter. Generally though, a certain filter-size is chosen because that is needed to avoid obstructing the lens but manufacturers also round up to common sizes to avoid forcing users to buy an excessive number of filters and line up with common filter sizes, although there are lenses which take filters in half-milimetre sizes too, presumably to be as compact as possible.
With a zoom lens, there is additional complexity that usually causes the filter size to be sufficient for the widest angle but more than enough towards the telephoto end. This is not true of all lenses as some zoom internally.
I just want to complement Itai's answer.
A step-up ring is a better scenario (having a 77mm filter on a 72mm thread)
But when the difference requires a lot of rings, let's say you need to use 8 rings, the filter is now further away from the lens, and some flaring could be noticeable.
Of course, the pro is that for expensive filters you could buy just a big one and get some adapter rings for some of your smaller lenses.
An alternative is getting a square filter system, where you only use one ring to be adapted to your lens at a time.