another, separate, other
另 centers on the idea of separation or distinction: something that is another, separate, or other. It marks a clear division between one thing and the rest.
另 combines 口 (mouth) and 力 (strength), but the historical origin of this combination is uncertain. It may have originally depicted separating or dividing with force, though the exact development is unclear.
A mouth 口 using strength 力 to split something apart: imagine biting off a piece and setting it aside as separate and other.
For レイ, picture a ray of light splitting a room into two separate spaces: ray -> レイ, and the light creates another distinct area.