Why is the image in a lens camera brighter than the image in a pin hole camera?

Think in terms of ray tracing. Light travels in a straight line in a pinhole camerabecause there is no refracting or reflecting optical element to change the path of the rays of light. The bottom of the film is on the line passing through the pinhole and top of the object. Since all light must pass through the pinhole, that means the top of the object exposes the bottom of the film.