Trivial answer: no, because you cannot center antimagic field on a pebble
Antimagic field can only be emanated from the caster him- or herself. You cannot cast it on other creatures or objects, the way you can with, e.g., light. Thus, the sequence you describe cannot take place.
Arcane archers1 and master abjurers2 can stick antimagic field onto other creatures, but not onto objects.
Trivial answer: no, the prismatic field destroys anything you try to bring in
Still, if you were an arcane archer or master abjurer, you could presumably tag some tiny-and-harmless critter with antimagic field (the master abjurer is much nicer about this process) and carry that instead of your pebble.
The violet veil is still going to just destroy it. It won’t make it to you, and the antimagic field will be annihilated along with the kitten (and you become a terrible person, if you were a master abjurer and not already).
Trivial answer: no, the antimagic field is in the prismatic sphere with you
OK, fine: assume an indestructable kitten, or at least one immune to the various effects of prismatic sphere.3
So you have your antimagic field-emanating kitten, you step out of the field (or never entered it, if you were a heartless bast— I mean, arcane archer), and you cast prismatic sphere. You now step towards the kitten, and the antimagic field is held at bay by your prismatic sphere. You step close enough to pick up the kitten,4 at which point your prismatic sphere is wholly enclosed inside an antimagic field. What happens?
The kitten is now inside your prismatic sphere. The prismatic sphere’s edge is a barrier through which the antimagic field cannot penetrate, but our amazing kitten can. Since the source of the antimagic field is now inside the prismatic sphere, it affects you, suppressing your magic, including the prismatic sphere, and freeing the antimagic field to extend to its full radius (rather than being limited by the inside of the prismatic sphere). Your prismatic sphere will return if and only if you step away from the kitten, allowing it to stay outside your prismatic sphere.
Real answer: antimagic field does not block magic, only suppresses it
Ultimately, the thing you were trying to do here is possible. The archmage’s Mastery of Shaping, for instance, could leave a 5-foot hole in the middle of the emanation that is centered on you, leaving you magical, with antimagic field around you. Unfortunately, that’s largely worthless, since magic can pass through an antimagic field. It doesn’t stop magic, just suppresses it while it’s in the antimagic field.
In game terms, antimagic field does not block the line of effect needed to target spells. So you are just as vulnerable to spells cast at you as you were without the antimagic field. Someone standing outside your shell can cast fireball at you, and the little red bead will disappear when it hits the shell – and reappear on your side of the shell, before hitting you in the face.5 Then it blows up, filling your hollow with fire, leaving your antimagic field-filled shell free of any flames, and yet more flames outside the shell.
All it really does is suppress the magic of those standing very close to you – which isn’t awful by any means, but it is a far cry from the invulnerability to spells you might imagine it is.
Also, casting prismatic sphere at this point does an interesting – but not particularly useful – thing. It limits the size of your antimagic field, basically defeating the Widen Spell metamagic you attempted to put on it. Instead of a 20-ft.-radius antimagic field with a 5-ft.-square hole in the middle, you end up with a 10-ft.-radius antimagic field with a 5-ft.-square hole in the middle, and a prismatic sphere around that. Even if you shrunk the prismatic sphere somehow, so it was inside the 5-ft.-square hole, your antimagic field won’t happen outside it.
If you do get a prismatic sphere with an antimagic field outside it, which can be done in more convoluted ways than I feel like getting into, spells can still go right through the antimagic field to attempt to cancel your prismatic sphere. But the prismatic sphere would not “wink out” because of the antimagic field around it, because antimagic field does not block magic, just suppresses it in the specific area covered by the field.6
Arcane archers can shoot an arrow that sticks a spell that ordinarily can only emanate from you, onto a target creature, who emanates it instead of you. The class feature was almost certainly written specifically for antimagic field; there are very few other spells where this would be desirable, but for antimagic field it is very desirable.
A “master abjurer” here is an abjurer who takes the master specialist prestige class in Complete Mage – their major school esoterica class feature allows them to cast abjurations that are normally centered on you (e.g. antimagic field) as a touch-attack spell that emanates from the touched creature. Again, antimagic field was almost-certainly the spell they had in mind when they wrote this.
Arcane archer, that doesn’t make what you did any kind of okay.
For the purposes of this answer, I am ignoring the fact that antimagic field and prismatic sphere have exactly the same size, and assuming the antimagic field is larger; assume Widen Spell was applied to antimagic field if it makes you feel better.
And if you are an arcane archer, you deserve it.
Even if antimagic field did block magic, it’s far from clear to me that the ambient magical energy necessary for spells wouldn’t still exist in the hollow – after all, I can have air inside a container whose walls block air. This is a setting detail that is not addressed by the general rules, and you would have to ask your DM.
There are two aspects to this question:
Why have material components that are free or inexpensive?
Why make them all different?
Why have Inexpensive material components
Most of the time, the presence of a free material component will just mean the caster needs to interact with an arcane focus or component pouch. They will need a hand free to do this.
There are spells that require no material component. These may be especially useful, for example, for a ranger with the War Casting feat, wielding a sword and shield or dual-wielding — he has no need to unwield a weapon or shield and then handle his component pouch (note, rangers do not get arcane foci) to cast such a spell.
Spells that lack one component or another can be handy when some game condition or other deprives them of the ability to use the component (that being silenced, bound, or deprived of a component pouch/arcane focus.)
Why have material components be unique, individual items?
While a few somatic or verbal components are specified in spell descriptions (notably, Burning Hands mentions touching one’s thumbs together) material components are specified in each spell’s stat block. Why?
Eye of newt, and toe of frog
One reason why this D&D tradition has survived (or been revived) is the same reason material components appear in Shakespeare: they do a good job setting a mood.
On the other hand, I think we could agree that calling out every syllable of every verbal component or gesture of every somatic one would simply be tedious.
Scrounging for components
If a caster doesn’t have access to a component pouch or arcane focus (generally because it was stolen or confiscated, but there might be other reasons) then individual components can play a role in game play. Some will be trivial to acquire, others difficult.
As such, they’re a little like encumbrance rules: some groups will never use them, many gloss over them most of the time — but they are there in case the situation calls for them. For example, Umbranus shares this memorable escapade:
In one game with an earlier edition my char could once save the party
after we were caught and tied up because I remembered how easy it is
to get the components for unseen servant. Back then it had no somatic
components but material component was similar to today: Piece of wood
and string. So I worked my clothes to pull a string out and scratched
the wood pole I was tied to until a piece came loose.
Without those
components this situation would not have been as noteworthy. And I
wouldn't still remember it.
Best Answer
I could find no developer commentary explaining why the spells needed to drop a prismatic sphere's or prismatic wall's layers were picked for any edition of Dungeons and Dragons that preceded Pathfinder, and Dungeons and Dragons 3.5e is whence Pathfinder takes its prismatic sphere, spray, and wall.
The prismatic spray originates with Vance…
Vance's short story "Mazirian the Magician" (1950) is the prismatic spray spell's source:
As can be seen from the description, Vance's the Excellent Prismatic Spray spell doesn't much resemble the effects of the D&D spell prismatic spray (from which Pathfinder drew its spell of the same name). Further, I've found nothing to indicate that the prismatic spray spell's effect was changed to distance it from Vance's creation, or, instead, that the spell was named as an homage to Vance's invention, or, really, anything much about the spell's development at all. But it's an almost inconceivable coincidence that the name's accidental, given Gygax's affection for Vance's works.
…But the prismatic wall and prismatic sphere don't seem to
While in the same story Mazirian uses the Spell of the Omnipotent Sphere, the D&D spell prismatic sphere doesn't seem to owe Vance's spell anything:
To this reader, that sounds closer to (but still different from) Otiluke's resilient sphere or something.
Thus it's my understanding and the understanding of others far more well-informed than I that the spells prismatic sphere and prismatic wall were created created wholecloth for Dungeons and Dragons, with no fiction serving as inspiration. Some things are just new, I guess.
Research notes
Originally—that is, in the Player's Handbook (1977) for Advanced Dungeons and Dragons, which is as originally as I can muster—the necessary spells were, in order of layers dropped, cone of cold, gust of wind, disintegrate, passwall, magic missile, continual light, and dispel magic.
However, in order of spell level for magic-user—AD&D's wizard—, these are as follows: 1st—magic missile; 2nd—continual light; 3rd—dispel magic, gust of wind; 5th—cone of cold, passwall; and 6th—disintegrate. This comes really close to a magic-user needing to devote one spell per spell levels 1st through 6th to drop a prismatic wall or sphere. (The last layer's being dropped by dispel magic remains an outlier but a reasonable one.) It'd be great if I could find a version of passwall or cone of cold that was, instead, a 4th-level spell, but, alas, I can't. (Even the 1974 Dungeons and Dragons puts its spell pass-wall as a 5th-level spell and lacks the spell cone of cold entirely!)
Were the spells needed to bring down a prismatic sphere or wall to equal one spell per spell level, this would be a predictable and interesting design choice, but there appears to be no point in mandating two 5th-level spells and one 6th-level spell: A level 10 magic-user can cast two 5th-level spells but no 6th-level spells, yet a level 12 magic-user can cast four 5th-level spells and one 6th-level spell, more than enough to drop a prismatic sphere or wall and have spells remaining!
Thinking this might be campaign-dependent, I looked for AD&D liches. While liches are (thankfully!) rare, encounters with level 17 magic-users in AD&D are rarer, and I thought perhaps an early adventure module might be geared toward level 12 or higher PCs encountering foes who could cast prismatic sphere or wall. But, for example, Asberdies, the infamous lich from Descent into the Depths of the Earth (1978) that's for levels 9–14, doesn't memorize prismatic sphere or wall, nor do the two liches (and, incidentally, the ki-rin) from the Rogue's Gallery (1980) (which includes PCs from Gygax's campaign). The spells needed to drop prismatic layers appear oddly—but, perhaps, appropriately—random. (I mean, seriously, what magic-user memorizes continual light instead of stinking cloud?)
In Dungeons and Dragons, Third Edition makes some changes, but keeps the same weird non-pattern. The spells, in order of layers dropped, become cone of cold, gust of wind, disintegrate, passwall, magic missile, daylight, and dispel magic. While some names changed, spell levels didn't, so that, in order of wizard spell level, this is as follows: 1st—magic missile; 2nd—daylight; 3rd—gust of wind; dispel magic; 5th—cone of cold, passwall; 6th—disintegrate. The Dungeons and Dragons 3.5 revision swaps the spell levels of daylight and gust of wind, keeping intact the same non-pattern.
Spell level isn't the connection. Spell school isn't the connection (a spell from each school would've been just as convenient!). Expected character level seems to have no impact. It doesn't appear to be a puzzle, either, as there's no reasonable acronym or initialism or apparent code. Some stuff we may just never know unless a designer deigns to reveal his secrets.