Analyze the complex symbolism and thematic significance of the recurring motif of the broken mirror in Sylvia Plath's seminal poem "Lady Lazarus." Discuss how this motif reflects the speaker's fragmented sense of identity and the poem's exploration of themes such as death, rebirth, and the nature of the self. Provide close textual analysis to support your interpretation, and compare and contrast this usage of the broken mirror symbol to its employment in other notable works of 20th century literature.​