What is the wisdom behind the waiting period ('iddah) for a woman whose husband has died, and is the waiting period obligatory for a post-menopausal woman, and what are its conditions, and why does the waiting period after divorce differ from the waiting period after death?

A woman who has despaired of menstruation observes the 'iddah (waiting period) of death (four months and ten days) or the 'iddah of divorce (three months). The sign of despairing of menstruation is reaching the age where menstruation typically ceases, which is often in the fifth decade of life. If a woman sees blood after the age of fifty, in line with her usual pattern, it is considered valid menstruation. For a woman who has not reached the age of despairing of menstruation and whose menstrual cycle has ceased, her 'iddah is a full year.