一般情况下是in the afternoon，但是，在有形容词修饰限制afternoon的时候，就要用on了。例如：He came in the afternoon.他下午来的。He came on a sunny afternoon.他在一个阳光明媚的下午来的。
例句
1、He's arriving in the afternoon
他下午会到。
2、He had stayed in his room all afternoon.
他整个下午都呆在房间里。
3、I was as tardy as ever for the afternoon appointments.
和以往一样，下午的约见我又迟到了。
4、Saturday afternoon is for recreation and outings
周六午后是休闲和外出游玩的时间。
5、I spent the remainder of the afternoon in play.
我把这一下午其余的时间用在游戏上了。