The range of the spell is listed as personal because it radiates from the caster and moves with it. But its effect is still a sphere so are still subject to the line of effect rule. So, a solid barrier would block it unless the barrier has a hole of at least 1 square foot through it. This also means that you have to be able to have a line of effect to the caster in order to dispel it.
I hate to do this, but I disagree with Mysterious Stranger on this one (sorry boss). The spell effects only the caster and has no "area" effect. (The area is the caster).
Line of Effect applies only to the casting of the spell, not what it does afterwards. Same with other 'communal' spells, Resist Energy, Communal doesn't stop working when you lose line of effect.
The "Sphere of Power" has an area, not the spell itself, which is self-only.
BTW: The Dispel Magic IS under the Line of Effect rule, so no, it can't be dispelled. My comment above is only in regards to the Invisibility Purge effect.
A sphere has an area, and creates an effect in that area. By definition that is an area of effect. If it does not have an area of effect the spell does not work.
There is also this line A sphere-shaped spell expands from its point of origin to fill a spherical area. Spheres may be bursts, emanations, or spreads. The line clearly states that spheres are bursts, emanations or spreads. Therefore, RAW Invisibility Purge is one of those even if it does not list it as such. Since all of them are subject to the line of effect rule, which one it actually is does not matter. If the spell could penetrate a solid barrier the description of the spell would have included that information.
Just to address the claim of RAW
RAW the spell has 3 properties:
Range: personal
Target: you
Duration: 1 min./level (D)
Range (personal) and Target (you) are obviously not affected by Line of Effect.
There is no "Effect" listed, so none of the rules under Effect apply.
There is no "Area" listed, so none of the rules under Area apply.
The only RAW that could possibly support a claim of Line of Effect needed for the 'effect' is:
You must have a clear line of effect to any target that you cast a spell on or to any space in which you wish to create an effect. You must have a clear line of effect to the point of origin of any spell you cast.
The problem with suggesting that is the applicable rule, is that "Line of Effect" is a rule for Spread, and Cone, Cylinder, Line or Sphere specifically, not for spells in general.
Truth is, Line of Effect isn't even a rule for targeting the casting. The rules for targeting are just you have to see or touch your target, and specifically choose that target. Line of Effect is first mentioned in Spread, but since Spread isn't an effect of the spell, that doesn't apply.
Thus, the only RAW rules we can use are the ones in the spell itself, which has the simple rule of: Anything invisible becomes visible while in the area. No direct mention of Line of Effect, as there are in other spells, such as Project Image.
You forgot to include the description of the spell. Just because the details are in the description of the spell does not mean they are not part of the spell
You surround yourself with a sphere of power with a radius of 5 feet per caster level that negates all forms of invisibility.
Anything invisible becomes visible
The first bolded portion of the spell defines the area, which is a radius of 5 feet per caster level. If that is not an area, I don’t know what is. The second bolded portion defines the effect and directly states it is an area.
You must have a clear line of effect to any target that you cast a spell on or to any space in which you wish to create an effect. You must have a clear line of effect to the point of origin of any spell you cast.
The section on line of effect is specifically mentions targeting spells. It also specifically states you need to have line of effect in any space you wish to create an effect.
If there is no area, how do you determine if an invisible character near you is affected by the spell? If there is no effect what does the spell do? The area of the spell is a radius of 5 feet per caster level, the effect of the spell is that anything that is invisible becomes visible.
Heh, no worries boss. Quite obvious you're not going to adjust your opinion on the matter. And I'm not about to go back to the age of trolling with large bold caps. :P
The OP has what he needs to either, as GM, decide... or as player, to argue the viewpoint he wants. :)
To the OP. Description is only used to introduce new rules, or counter existing rules. Nothing in this description counters any existing rule, nor does it give the spell an 'area', despite having used the word in the description. Similar to spells like Antipathy, which despite doing things to an area, don't require Line of Effect.
That's all I'll say on the matter, you decide how it goes in your game (or how you want to argue it for your character). :)