The Slit lamp was invented by Allvar Gullstrand from Sweden in 1911 with Carl Zeiss of Germany using the Nernst electric bulb. The filament was focused upon a slit and that produced a rectangular beam of light that could be brought to sharp focus on the eye by an aplanatic lens.
The idea was to illuminate the interior of the eye with a slit of light rather than with collimated light which was the usual with microscopy at the time.
In 1916, Carl Zeiss combined the slit lamp with the binocular corneal microscope developed by Siegfried Czapski in 1899 for Carl Zeiss. They were coupled around the same axis.
Further improvements came in 1933 by Goldmann. He connected the slit arm and microscope on a single supporting column. Also around 1933, the Comberg design had a common swivel axis for the microscope and illumination. The slit lamp now stood vertically reducing the need for light carrying rods. The 1950 Littmann design featured a magnification changer.
Allvar Gullstrand (1862-1930)–the gentleman with the lamp. Acta Ophthalmol. 2011 Dec;89(8):701-8
Allvar Gullstrand and the slit lamp 1911. Ir J Med Sci. 2013 Jun;182(2):301-5