Reflecting Meduim : Intellect / Mind (part of subtle body - unreal)
Reflection : Jiva (in absolute reality not different from Brahman)
As I've discussed in previous answer Jiva is the Upadhi superimposed on the intellect. So, intellect/mind (under the influence of may or due to ignorance) is the reflecting medium. And Jiva is different from subtle body.
According to Shata Shloki of Adi Shankaracharya:
50. Brahman reflected in the intellects of various bodies such as those of human beings, animals, birds, etc, takes those forms. The one person reflected in water appears as two, the original and the reflection. Similarly, the one Supreme Being (Brahman) takes on, by His power of Maya, innumerable forms because of being reflected in innumerable intellects. So says Br. Up. in 2.5.19. The all-pervading (and non-dual) Brahman appears, inscrutably, due to Maya, as the Jiva, by being reflected in the limiting adjunct (upadhi) in the form of the intellect which, being constituted of Sattva alone, is pure and so capable of reflecting Brahman.
The jiva being a reflection of Brahman, is in reality non-different from Brahman. The Jivas appear as many, different from one another and limited beings, only because of the limiting adjunct, the intellect, just as the space inside a pot, though not different from the total infinite space, appears to be limited by the size of the pot.
But here it should be noted that the Brahman isn't being distorted or transformed.
51. The men of realization perceive that the Jiva, who is a reflection of Brahman in the subtle intellect, is in the grip of the Maya of the supremely powerful Lord. The nature of the reflection of Brahman, that is to say, the nature of a particular Jiva, depends on the nature of his intellect (or mind), just as the reflection of a face in a mirror varies according as the mirror is convex or concave, clean or covered with dirt, fixed or moving. But, just as the face itself is not in the least affected by the nature of the mirror, so also, Brahman is not at all affected by the nature of the reflecting medium, the mind, and ever remains the same and immutable.