He is in fact delighted!  Making clear verifiable Progress is fun, and dath ilani are heavily shaped away from taking offense at corrections, in their high-trust society where corrections are rarely offered for malicious reasons.

PL-timestamp:  Day 25 (21) / Mid-Afternoon

All right, you primitive screwheads, listen up!  This is now day three of trying to build a spectroscope.  Back in dath ilan, any startup that failed to build a prototype of anything in three days would be shut down by its funders as clearly hopeless.

Keltham was specifically hoping to have a spectroscope on hand while evaluating hiring and tiering, so he could see who was making the most progress at learning to shift the electron-orbital behavior of materials using Prestidigitation of color-taste-smell-stickiness.

Their present situation may be summarized as follows:

They don't have a professional glassmaker on-site, nor on-site glassmaking equipment to build a prism out of optical glass.  Specifying and ordering a prism from off-site would probably take several days and probably not be quite right on arrival.

They have a large piece of cloudy quartz that was successfully Stone-Shaped into the right rough shape of a prism, and then further cut flat with overkill magical slicing spells.

Despite Prestidigitation supposedly being able to change the color of things, Keltham has not been able to clear this quartz in a way that makes it suitable for use in a spectroscope's prism, nor change the flat surface of it into a diffraction grating.

They have tiny pieces of nice clear quartz that would, if they were larger, probably work to build a spectroscope.

Keltham's plan is therefore as follows:

Step one, use their spectroscope to burn a piece of clear quartz and get a reading from the spectral lines off that.

Step two, other people will practice Prestidigitating bits of cloudy quartz 'clearer', burning those under their spectroscope, and trying to shift the absorption lines of cloudy quartz towards being entirely the dominant spectrographic lines recorded from the clear quartz.

Step three, Prestidigitate their large shaped piece of quartz clear, and use it to build their first spectroscope.

Step four, send their spectroscope back in time to step one.

Now, Keltham isn't sure that part will work, but, if Civilization's teachings about the fundamental nature of reality are true, it shouldn't be that hard for him to use Prestidigitation to create a small time-loop -

"VETO."

"VETO."

"I agree in these objections."

"If the only problem with the diamond is that it's too small we can get a True Resurrection grade one, they're about thrice as large across."

"Why would you even say that in public, Keltham, why in Pharasma's name would you?"

The problem, Lady Avaricia, is that they don't just need a size, they need a shape, and even thrice as large across would probably not be large enough -

"Okay, he's trolling."

"Correct!  Though we do, fundamentally, have a problem where we could maybe use a spectroscope to build a spectroscope but we don't have a spectroscope and therefore can't use a spectroscope to build the spectroscope we'd need in order to build a spectroscope."

"Besides time travel, can anybody else think of an obvious solution there?"

Gregoria's thinking she missed what was wrong with the solution where they wait a couple days for a glassmaker to send them some attempts at following their instructions.

"What I'm actually going to do is use Silent Image to create illusions of spectroscopy stations for everyone.  If a Silent Image of a mirror works as a mirror, a Silent Image of a spectroscope should work as a spectroscope, or so I reason.  If an illusionary mirror works as a mirror, a light-exclusion hood should work as a hood, a light source should work as a light source, and a prism should work as a prism."

"I'll also create illusions of prisms the correct size and shape to do the job, illusions of evenly frequency-distributed light that's good for testing absorption lines, and illusions of diffraction gratings."

"I'm going to maintain my concentration on that for as long as I can, and, before the spell ends, you need to manage to either Prestidigitate quartz to clarity, or Prestidigitate a surface to behave like a diffraction grating.  If possible, also Prestidigitate a light source to behave like an evenly-frequency-distributed light source, but that may legit be harder."

"And if we can't get that done today - take note of how far you got in deliberately shifting the frequency lines, where you started, where you ended up, and how much progress you made."

"Assuming, of course, that this whole clever plan does not completely utterly fail on step zero."

"Carissa, you said you had an illusion spell prepped, right?  You're on learning to make your own illusionary spectroscopes that work, in case we're stuck with illusionary spectroscopes for a while, so that I'm not the only one who can cast them using my one first-circle wizard spell per day.  I mean, fine if you can teach others here after that, but you being able to learn it yourself would give us some breathing room.  You have good concentration."

- sure, she'll try to learn that. 

This seems like the kind of thing that couldn't possibly work but they'll try it.

Cleverness results:

- Keltham's spectroscopy stations sort of suck; not really in a way where they work, per se.  But maybe in a way where they literally work at all and you can try to guess where the spectral lines might maybe possibly be?

- They can't get their shaped quartz clear to where it's better than the sucky spectroscopy station's illusionary prism, but they're getting it clearer.

- Carissa learned how to make illusions of Keltham's illusionary spectroscopy stations, and her illusions of his illusions are at least no worse.

- Diffraction gratings are really neat, nobody besides Avaricia has ever seen that rainbow-holographic sheen before on something that isn't an oil slick or in some cases an absurdly expensive magic item, buuut they can't Prestidigitate a surface with that 'color' well enough for it to work inside a spectroscopy station.

Ione will, at some point, wander over to the visible Security and ask him if he's by any chance got a Major Image or at least Minor Image prepped today.

Security does have Major Image prepped. 

If he can maintain concentration for a while, how about if they throw a Major Image specifically at creating an illusion of a clear glass / clear quartz prism, the same size and shape of Keltham's rougher Silent Image of a prism.

- sure, he can do that. They don't put you on Security if you can't concentrate on an illusion and also do your job.

Great.

How about if Sevar dispels just the prism part of the illusion that she's maintaining of a spectrography workstation, and then Security puts his Major Image of an illusionary prism where that prism used to be?

Sure.

Carissa's illusion of Keltham's illusion of a light source sure is going into Security's illusionary prism and making a nice rainbow on Carissa's illusion of Keltham's illusion of a display axis marked with unreadable wavelengths because Silent Image isn't fine enough for writing!

"So, uh, Sevar, do we tell Keltham we've got a working spectography station and risk disturbing his concentration, or..."