Final answer:
The Duke in Robert Browning's "My Last Duchess" shows indifference to his wife, obsessing over social status and reputation rather than family relationships. He exhibits controlling behavior, jealousy, and a disregard for his wife, fearing any damage to his status.
Step-by-step explanation:
Examining the dramatic monologue spoken by the Duke in Robert Browning's "My Last Duchess," we can infer that the Duke's character aligns most closely with option (b): he is indifferent to his wife and cares primarily about his social status and reputation. He fears being embarrassed by her behavior.
The Duke repeatedly emphasizes his concern for maintaining control over his environment and the people in it, becoming irritated when his wife treated his 'gift of a nine-hundred-years-old name' as equal to any other attention or kindness she received from others. Jealousy and possessiveness are also evident when he speaks of the smiles his wife gave freely and how 'twas not her husband's presence only, called that spot of joy into the Duchess' cheek.' It elucidates his obsession with exclusivity in her appreciations, indicative of his aristocratic arrogance.
The Duke's disregard for his late wife's individuality and well-being is clear when he narrates how he gave commands and then all smiles stopped together, suggesting that her life ended due to his orders, reflecting his prioritization of authority over compassion.
Thus, the Duke's fears center not on personal loss but on the potential damage to his reputation and the expectations of unwavering deference to his social rank.