This is a lens for a 16mm film projector. It has a 2 inch (51mm) focal length.
Compare it to similar Bell & Howell 16mm film projector lenses, such as this one for sale on eBay.
Assuming the lens's image circle is not substantially larger than the diagonal of 16mm film format (which has a nominal size of 0.380 in by 0.284 in), then compared to 35mm photographic film format, it will have a crop factor of 3.6. Thus, the ~51mm lens, after you crop your images to remove the smaller projected image, would have the same approximate angle of view as a 180mm lens on a full frame camera. Again, this assumes the lens's image circle is relatively tight to the diagonal of 16mm film.
If you're willing to accept some vignetting, the image circle projected is probably quite a bit larger than strict 16mm format. I would guess a crop factor of about 2.5, or even as low as 2 (if you're willing to accept lots of "artistic" vignetting).
In order to adapt this to your E-mount, you will need some means of focusing this. Some examples:
Mathieu Stern used a 50mm f/1.2 Bell & Howell projector lens simply slipped into a macro extension tube (which was a loose fit). He simply manually moved the lens forward or backward to focus. YouTube link; PetaPixel article discussing the video.
User nukemall at mflenses.com forums shows an interesting solution: a Russian 50mm focal length 16mm projector lens fitted into a scavenged Helios 44M-4 body (with glass and aperture removed) to use as a focusing helicoid, with the mounting flange replaced by a Sony E-mount bayonet.
User nigbat at dpreview.com forums shows a 50/1.4 16mm projector lens mounted inside a M58 helicoid with a Micro Four Thirds lens mount adapter. It looks like the helicoid was drilled and tapped to accept three hex cap screws to hold the projector lens in place.
- Note: the poster says that the lens does not vignette noticeably on his MFT camera (which has a crop factor of 2×). Whether that is common amongst all 16mm format projector lenses, or the particular one used by nigbat (a Singer Graflex), I don't know.
User GnarlydogOZ at dpreview.com forums has a Bell & Howell 50/1.6 2" projector lens shimmed with PVC pipe into a M39-to-M42 adapter, mounted on a Vivitar M42 bellows, which is mounted to his Olympus MFT camera.