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If you were outside during the day and you cast darkness above you somehow, would the darkness spell cast a shadow?
If you cast darkness in a tunnel, and the only source of light was from one end of the tunnel only, would the other side of the darkness spell remain illuminated or would it be plunged in shadow (non-magical darkness)?
The description of the darkness spell says that "light can't illuminate". I would therefore posit that it also does not pass through it either.
No, darkness doesn't cast a shadow.
At least, it doesn't without a particular DM making it a table rule — which would be a totally reasonable ruling to make. To tackle the question though, we must consider the default baseline from which such rulings would be made, avoiding assuming rulings that give us a result from circular reasoning.
Darkness not casting a shadow is non-intuitive, but magical darkness is inherently non-intuitive and operates by its own idiosyncratic rules.
I've emphasised the relevant parts of its effect description (PBR p. 86; PHB p. 230):
Magical darkness spreads from a point you choose within range to fill a 15-foot-radius sphere for the duration. The darkness spreads around corners. A creature with darkvision can’t see through this darkness, and nonmagical light can’t illuminate it.
The stipulation that it's effect is limited to a radius of 15 feet, and that its effect is to prevent illumination, not penetration of light, means that it does not and cannot alter light levels outside its area of effect.
Contrast this effect description of darkness with that of fog cloud: the latter's description simply says that it creates fog in a given area, and then leaves it as an exercise for the reader to extrapolate from our shared understanding of real-world fog — such as the fact that fog impedes the passage of light — with the help of the game's specific rules for obscured vision. Darkness, by contrast, does not try to leverage our intuitions about "magical darkness" — as none can be expected of us1 — and instead gives specific effects. These effects are sufficient for most groups, so that groups who don't care (or who prefer a non-scientific fantasy experience) can get on with the game without having to tackle the question "but how does it work?!" with lengthy deliberations first.2
It could be argued that the line "A creature with darkvision can’t see through this darkness" means that light is entirely prevented from passing through. However, such an extrapolation would be a ruling limited to the ruling DM's game, as other DMs will not all also make the same ruling. (Since how darkvision operates is idiosyncratic and non-lawlike in the same way as how magical darkness does, we cannot reason from how it operates to how darkness operates, without a DM adding even more interpretive rulings.) Since such a ruling is an addition and not universal to all possible DMs, and because magical darkness is inherently illogical, that extrapolation can't be considered the default, baseline case.
1. Those of us who have a specific metaphysical reality in mind that does create intuitions about how magical darkness operates are precisely those who would want to make rulings about darkness in order to satisfy our intuitions and to make the spell better match our imagined setting. This is exactly what the permission to houserule, that the game gives DMs, is designed to accommodate. For the rest of us, the game doesn't assume anything, and gives us bare effects for things that are not transparent to the usual intuitions of modern humans, like darkvision and the darkness spell.
2. In my own games, I'm likely to rule that it does cast a shadow because I tend toward classicism in my campaign metaphysics — if the issue ever comes up, which I expect it likely won't. Except that, if I'm running a romanticist campaign based on my ontological Chaos premise, I'm likely to say that it doesn't cast a shadow and neither does its contents, for no reason other than "because Chaos." So, there you go: it very much depends on the DM and campaign.
When I first read the spell description, I also was surprised about the:
« [...] nonmagical light can't illuminate it. »
At the same time they say that magical light created by a cantrip or a spell of level 1 or 2 will be dispelled, which I would interpret as: « Any light entering the darkness area is destroyed. »¹
That, in effect, means anything behind a darkness area would also be in the dark / shadow.
Unfortunately, the 15-foot-radius sphere is not said to be shrinking. If it were, we could imply that the light and darkness are annihilating each other up until the point were the darkness is gone.
Also, because of diffraction², whether a sphere of darkness would cast much of a shadow outdoor, I would say probably, but really not much. You could try with a d20 and see that the shadow is really not much unless you are really close to the ground. On the other hand, I would say that such a darkness sphere in a corridor totally blocks the light if the sphere fills the corridor.
Now... there is an interesting point, if you cast the darkness on an object such as a stick, you can then place an opaque object over that stick in order to block the darkness! Very similar to having a hooded lantern and closing the hood. Yet, a creature does not seem to be considered opaque enough to block the darkness...
¹ I think to remember that AD&D (1e) was clearly saying that all light was destroyed when entering the darkness area. Unfortunately, I do not have the books anymore.
² Note that diffraction really needs some form of material to work. I would think that Darkness can't be considered matter...
The Darkness spell absolutely casts shadow.
Consider these options 1 and 2 with a character hiding inside the darkness:
1: If darkness didn't stop light from passing through, then the character inside the area would cast a shadow (and be seen as a shadow at least), unless the spell works like a cloaking device by wrapping light around it. In that case the area wouldn't be seen dark, but translucent, and there is actually another spell that have this kind of effect and it's called invisibility.
2: The spell creates a 15-foot sphere, which no light can pass (except high level magical one). The area would look like total darkness to the eyes and it would also cast shadows, because it blocks light. The character inside the sphere can not be seen (or see, unless they have Devil's sight).
The very notion that it is a sphere of darkness (darkness that spreads to fill a sphere) assumes that light can't go through, otherwise the sphere itself would be transparent. It has to absorb light to appear as darkness. And obviously, if light can't pass through it, it casts a shadow.
