Final answer:
The question seems to confuse characters from different contexts. Without the correct literary source, a detailed analysis of Smirnov and Mrs. Popov's interaction related to mourning cannot be provided. The quote provided is not sufficient to determine the context or the reason Smirnov would doubt Mrs. Popov's mourning plan.
Step-by-step explanation:
The mention of Smirnov doubting Mrs. Popov’s mourning in the provided quote seems to be a case of mistaken context, as the quote actually discusses a character named Winterbourne and his interaction regarding a mother, possibly not seeing someone due to feeling guilty about a shawl.
This suggests a potential scene from a social or dramatic interaction rather than a specific challenge to a mourning plan. Without additional context, it is not possible to provide an accurate and detailed response regarding Smirnov, Mrs. Popov, or the specifics of any alleged mourning plan.
It would be essential to know the exact source material being referenced, such as a play, story, or another work of literature that features these characters and their interactions. If the reference is indeed toward a specific work that includes Smirnov and Mrs. Popov, for instance, Anton Chekhov's comedy “The Brute” or “The Bear”, there may be a relevant discussion about mourning and its genuineness.