I just read an excellent description of a bulls-eye lantern, or dark lantern, in Patricia Cornwell's
Here are a couple brief excerpts:
...a dangerous, cumbersome device comprised of a steel cylinder ten inches high. ... The magnifying lens wass three inches in diameter and made of thick, rounded, ground glass, and inside the lamp were a small oil pan and wick.
(the author lights the lantern and) ...I held my hand in front of the lantern and at a distance of six inches could barely see a trace of my palm....
...The typical Victorian may not have had a clue about the inadequacy of bull's-eye lanterns. Magazines ... showed constables shining intense beams into the darkest corners...
The author explains that, in the nicer parts of town, the lanterns were unneccessary. Only in the "forbidden places" did constables carry these lights, and most people didn't venture into those areas.
oristar (or anyone else), if you wish to learn more about London in this period (late 1880's), this book is an excellent, well-researched source. At the time of the Ripper murders, the stage play of Dr. Jeckyll and Mr. Hyde
was very popular, and is mentioned several times.