illusion vs pie in the sky

illusion

noun
  • A misapprehension; a belief in something that is in fact not true. 

  • Anything that seems to be something that it is not. 

  • A magician’s trick. 

  • The state of being deceived or misled. 

pie in the sky

noun
  • A fanciful notion; an unrealistic or ludicrous concept; the illusory promise of a desired outcome that is unlikely to happen. 

How often have the words illusion and pie in the sky occurred in a corpus of books? (source: Google Ngram Viewer )