We are talking 5e here, a Sorcerer sits by the fire, hears someone approach (thanks to a previously set alarm spell) but does not see them. He casts a subtle spell (no somatic or verbal) of See Invisibility.

Now approach-ee who is invisible has knowledge Arcana (I'll call him Arcanist from now on): would he know the spell was cast?

I understand if the Sorcerer cast a fire ball, invisible Arcanist would definitely know. I imagine that metamagic exists so you are more subtle, but under strict observation with no distractions, would the Arcanist understand what happened?

(Since it wasn't a high tension situation, I handled it with the perception check of DC20, the invisible Arcanist saw a glimmer in the eyes, and I suggested he realized there was something to do with vision but naught else).

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    \$\begingroup\$ It doesn't really matter that much, but is either the sorcerer or the arcanist a PC? \$\endgroup\$ – NautArch Jan 21 '18 at 16:37

It depends if the Arcanist was able to see the sorcerer while the spell was cast

Xanathar's Guide to Everything has some suggested rules for identifying spells and casting on page 85.

To be perceptible, the casting of a spell must involve a verbal, somatic, or material component...If the need for a spell's components has be removed by a special ability such as the sorcerer's Subtle Spell feature or the Innate Spellcasting trait possessed by many creatures, the casting of the spell is imperceptible.

See Invisibility has a material component, which isn't removed by subtle spell. So, the casting of the spell is, by a strict reading of these rules, perceptible. Xanathar's guide gives extra rules on identifying a spell on the same page.

If the character perceived the casting, the spell's effect, or both, the character can make an Intelligence (Arcana) check with the reaction or action. The DC equals 15 + the spell's level.

So the DC is 17 if the Arcanist can see the casting of the spell

See Invisibilty is 2nd level, and 15 + 2 = 17. However, See Invisibility does not, rules as written, have any visible effect. There is no "glimmer in the eyes" as written. You just see invisible things. That makes the spell's effect imperceptible after the spell is cast. Because of that, the Arcanist needs to see the spell being cast to have a chance to identify it. Otherwise, he's out of luck.

Identifying a spell is impossible if the casting and effect are imperceptible

Note that the only reason the Arcansit even has a chance to identify the spell is because See Invisibility has a material component. This gives him the chance to witness the casting of the spell. However, if the casting of the spell was imperceptible (either due to a lack of components, or because he couldn't see it from his location) and the spell has no perceptible effect (such as See Invisibility) then they cannot meet the requirements to identify a spell, and he shouldn't be make any check at all.

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    \$\begingroup\$ I think it should be noted that an arcane focus can replace material components and can be held in the same hand that you use for the somatic component. If the sorcerer already had a focus in his hand, there would be no material component to witness. Making the subtle casting of this spell imperceptible. \$\endgroup\$ – Luke Jan 22 '18 at 4:00
  • \$\begingroup\$ Perhaps add a note about how it would change if it was nighttime (which is implied but not explicit in the situation in the question). \$\endgroup\$ – SevenSidedDie Jan 22 '18 at 4:40

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