What is imagination?
I feel like there is no right and wrong answer to this question, as people are different and perceive things differently. One person might project an image of an apple in their mind like you gave the example of. Another might imagine an apple and get a ghost taste of an apple on their tongue. Yet another might simply see the word 'apple' flash in their mind's eye.
Though I like your definition for imagination: "A personal power for projection"
Another point regarding Imagination is that in this day and age with so much access to constant stimulation, video games, movies, social media etc, we are rarely bored and so have no need for our imagination. I wonder if as society 'develops' our collective imaginations will begin to die off.