The range section of the PHB says:
This lists the distance from the caster at which the spell effect occurs or begins. [...]Unless otherwise specified, [...] spells [other than those with a range of 0 or touch] are centered on a point visible to the caster and within the range of the spell. [...]Spells can be cast through narrow openings only if both the caster's vision and the spell energy can be directed simultaneously through the opening.
A wizard standing behind an arrow slit can cast through it; sending a fireball through a small peephole he is peering through is another matter.
Magic Missile says:
Range: 60 yds. + 10 yds./level
Area of Effect: 1-5 targets
Use of the magic missile spell creates up to five missiles of magical energy that dart forth from the wizard's fingertip and unerringly strike their target. This includes enemy creatures in a melee. The target creature must be seen or otherwise detected to be hit, however, so near-total concealment, such as that offered by arrow slits, can render the spell ineffective. Likewise, the caster must be able to identify the target. He cannot direct a magic missile to "Strike the commander of the legion," unless he can single out the commander from the rest of the soldiers. Specific parts of a creature cannot be singled out. Inanimate objects (locks, etc.) cannot be damaged by the spell, and any attempt to do so wastes the missiles to no effect. Against creatures, each missile inflicts 1d4+1 points of damage.
For every two extra levels of experience, the wizard gains an additional missile--he has two at 3rd level, three at 5th level, four at 7th level, etc., up to a total of five missiles at 9th level. If the wizard has multiple missile capability, he can have them strike a single target creature or several creatures, as desired.
If within range, then the missile would hit, as the caster has line of effect through the open corridor, and can see and identify the target. If he can identify and specify his target, and the target is not concealed from sight, then the missile(s) unerringly hit their target.
The characters will see the missiles arc around the corner, and may also notice the missiles' reflections as they approach and then pass the mirror.