What purpose is served by introducing Mrs. Rogers as a frightened "ghost" of a woman?
The purpose the author has of introducing Mrs. Roger as a frightened ghost of a woman is to add a sinister, foreboding feeling to the atmosphere. Vera had just walked into a delightful bedroom with a big window and was very pleased. Mrs. Rogers escorted her there. But when Vera looked at Mrs. Rogers closely, she thinks Mrs. Rogers is very pale and "bloodless". Although she was quite respectable and dressed as a maid, she had
"Queer light eyes that shifted the whole time from place to place" (pg 31)
Vera thinks she looks frightened of something and that idea gave Vera a physical reaction, it made a shiver run down Vera's back. She says that
"She looked like a woman who walked in mortal fear..." (pg 31)
The word mortal means subject to death. (See link) It gives the reader a feeling of dread of some kind of evil force or forces on the island that are going to cause someone's death. When Mrs. Rogers turns to leave the room,
"Her feet moved noiselessly over the ground. She drifted from room to room like a shadow" (pg 32)
That is another reference to a ghost.
The pages of the book may differ depending on which edition you are reading, but the words should be in the general vicinity of the pages listed.