Replace your old peephole with one of the newer in-door viewers. It's a low-cost solution that uses prisms and a lens to project the visitor's image onto a 2-in. screen. The large screen allows you to see visitors from 5 to 7 ft. behind the door. You can find in-door viewers with an internet search for “in-door viewer”.
You'll have to drill a new 2-3/8-in. hole. Place it so the new hole eliminates the existing hole at the same time. You can probably leave the old peephole in place while you drill the new hole (to provide a firmer surface and prevent pilot bit wandering). Make sure the drill is level and drill until the pilot bit comes out the other side of the door. Then remove the hole saw and drill from the opposite side (to prevent splintering). You’ll also need to drill two 1/8-in. holes for the retaining ring anchor pins (use the template to mark the location for the small holes). To finish the installation, insert the viewer and screw it onto the lens prism.
The new viewer provides a much brighter image, but since it uses prisms, be aware that the image will be flopped left to right. As an added benefit, the viewer optics prevent visitors from peering into your house (a flaw in old-style peepholes) or from noticing that you're even using the viewer.