Is it possible to affect targets with spells from the other side of an anti-magic field?

Question

Suppose a short, 5'x5', 20' long open corridor separates two rooms, with no other features besides that inside the corridor was the source of an active Antimagic Field.

If your Wizard cast Magic Missile from one room at a target within range and in the other room, both outside the AMF, what would happen?

Now the Wizard casts Fireball at a ground target near some enemies in the other room. What happens?

Same again, but now the Wizard casts Cone of Cold to include a target within range and line of sight in the other room. What happens?

Finally, the Wizard casts Polymorph (sheep) at a target in the other room. What happens?

Answer 1

Antimagic Field only affects its own area

Specifically:

Targeted Effects: Spells and other magical effects, such as Magic Missile and Charm Person, that target a creature or an object in the Sphere have no effect on that target.

Areas of Magic: The area of another spell or magical effect, such as Fireball, can't extend into the Sphere. If the Sphere overlaps an area of magic, the part of the area that is covered by the Sphere is suppressed. For example, the flames created by a Wall of Fire are suppressed within the Sphere, creating a gap in the wall if the overlap is large enough.

Providing that you meet the targeting requirements of the particular spell (the default being a clear path to the target [check] and being within range) then the antimagic field does not prevent you from targeting a spell through it.

So:

1. The Magic Missile hits.
2. The Fireball works except that any part of its area of effect that overlapped the Antimagic Field would be suppressed.
3. The Cone of Cold works everywhere except where it overlaps the Antimagic Field
4. With the Polymorph, if the creature is willing or fails its saving throw it is now a sheep.

Answer 2

Spells can be cast through the Antimagic Field

I agree completely with DaleM's answer but thought I might provide a different way of getting to the same answer.

Antimagic field does not block or change the targeting rules

There is nothing in the spell effect description that says that antimagic field has any effect on the ability to target things magically or mundanely through it. In fact, antimagic field does not even have any effect on the ability to target things inside of the AMF.

Targeted Effects: Spells and other magical effects, such as Magic Missile and Charm Person, that target a creature or an object in the Sphere have no effect on that target.

The only change antimagic field makes is that creatures targeted with magical effects while inside of it are not affected by them.

Thus, the normal rules of targeting apply and antimagic field does not change them at all.

Magical effects crossing into the AMF are suppressed, but not dispelled or blocked

Spells and other magical effects [...] are suppressed in the sphere and can't protrude into it. A slot expended to cast a suppressed spell is consumed. While an effect is suppressed, it doesn't function, but the time it spends suppressed counts against its duration.

In this case, "suppressed" is being used to mean that the effect stops working while it is in the field. Note specifically though that it does not dispel or block any effect. The effects simply stop working in the AMF. Spell durations still count, concentration still has to be maintained, etc. If the AMF actually blocked or dispelled these things, the spell description would say that instead.

Light

So, to take a simple example, if I were to cast light to create a magic effect on a rock in my hand and walk into an AMF, it would stop glowing. However, as I came out the other side of the AMF it would immediately light up again (assuming I am still within the duration of the spell).

That same principle applies to any magical effect passing through the AMF.

Fireball

So, fireball for example would, upon being cast, essentially travel from the caster's finger through the AMF (becoming invisible in this area) and then becoming visible again before hitting it's target on the other side of the AMF. Of course, because fireball is an AOE effect it is effected by another clause of antimagic field's description:

Areas of Magic: The area of another spell or magical effect, such as Fireball, can't extend into the Sphere. If the Sphere overlaps an area of magic, the part of the area that is covered by the Sphere is suppressed. For example, the flames created by a Wall of Fire are suppressed within the Sphere, creating a gap in the wall if the overlap is large enough.

So if the actual fireball that results from hitting its target overlaps with the area of AMF then there is no fire in that area.

And this is explicitly according to the rules laid out in the description of antimagic field.

Specific questions

Applying this to your specific question yields the following:

1. Magic missile would hit.
2. Fireball would hit its intended target (and any AOE overlap with AMF would be suppressed)
3. Cone of cold would be cast as expected (any AOE overlap with AMF would be suppressed)
4. Polymorph takes effect if the creature meets the conditions in the spell (failed saving throw or willing)

Answer 3

It depends on the spell

The relevant portion of Antimagic Field is

Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it.

As such, here's what happens for the spells you listed (keep in mind the field does not provide total cover so all targets are eligible for selection, even if the spell doesn't work as intended):

Fireball

A bright streak flashes from your pointing finger to a point you choose within range...

The streak of light heading towards the target spot is suppressed and the fireball never activates.

Magic Missle

Each dart hits a creature of your choice that you can see within range.

Nothing specifies the direction or origin of the bolts so they can hit the target.

Cone of Cold

Needs a bit more text to clarify.

Antimagic Field:

The area of another spell or magical effect, such as Fireball, can't extend into the sphere.

Area of Effect (Cone):

A cone extends in a direction you choose from its point of origin.

Cone of Cold:

A blast of cold air erupts from your hands.

Since the point of origin is your hands, it can't extend past the Antimagic Field.

Polymorph

This spell transforms a creature with at least 1 hit point that you can see within range into a new form

Like with Magic Missle, there is nothing for the Antimagic Field to supress so the spell works.

Answer 4

RAW Depends

The spell description for antimagic field

A 10-foot-radius invisible sphere of antimagic surrounds you. This area is divorced from the magical energy that suffuses the multiverse. Within the sphere, spells can’t be cast, summoned creatures disappear, and even magic items become mundane. Until the spell ends, the sphere moves with you, centered on you. Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can’t protrude into it. A slot expended to cast a suppressed spell is consumed. While an effect is suppressed, it doesn’t function, but the time it spends suppressed counts against its duration. (PHB pg 213)

Bolding mine

So basically when you cast these spells some will have a physical movement in their spell description like fireball's small ball of flame and magic missiles 3 darts. when these move through the antimagic field they disipate and have no effect. Polymorph and similar spells don't specify a physical form so would work.