Pesachim 11 - When one missed his search for chametz
If one missed the right time ( night of the fourteenth of Nissan ) to search for chametz, what is he to do? Rabbi Yehudah says that he can search in the morning of the next day, and even later, until midday, up until the time when chametz becomes prohibited. However, the Sages allow one search in the morning, and in the appointed time, and even after that. Why does Rabbi Yehudah stop the search after the chametz becomes forbidden? - Because he is concerned that people may accidentally put it in their mouths. And the Sages? - They say that since one is looking for chametz to destroy it, he will surely not eat it.
What is the "appointed time?" above. Rashi says that this is the time appointed for search, before Pesach. But the Tosafot say that this is the time of the Pesach celebration itself. Thus we have very divergent opinions, with Tosafot requiring to search for chametz all the way through Passover and even after that! What causes such a big disagreement? Rashi considered the purpose of the search to stop people from owning chametz on Passover; after Passover has started, chametz is legally not theirs anyway. But Tosafot say that the purpose of the search is so that people would not eat prohibited chametz, and chametz even after Passover can be prohibited, if a Jew owned it.
Art: In Search of Medicine by Vladimir Egorovic Makovsky