why do you think that it takes so long for the family to realise that they may each be looking at a different photograph

Realizing that they could each have been shown a different photograph, and after calling the Chief Constable to confirm their suspicions, Mr. and Mrs. Birling and Gerald conclude that they have been hoaxed, and they are incredibly relieved. Gerald suggests that there were probably several different girls in each of their stories. They call the Infirmary and learn delightedly that no girl has died that night—the Infirmary has seen no suicide for months. Everyone, it seems, is off the hook, even if each of their actions was immoral and irresponsible.