What was this optical apparatus called? (It was used for showing pictures.)
Wikipedia page, linked here, shows a list of images related to peep-show (also known as peep box, raree show, or Perspective View). All images (except the sketch) tagged in the question can be seen in this link.
Peep-show
a display of objects or pictures viewed through a small opening that is usually fitted with a magnifying lens.
a short, usually erotic or titillating film shown in a coin-operated viewing machine equipped with a projector.
So there's a high chance that people will take it to mean the second definition.
Peep-show on Wikipedia:
A peep show or peepshow is an exhibition of pictures, objects or people viewed through a small hole or magnifying glass. Though historically a peep show was a form of entertainment provided by wandering showmen, nowadays it more commonly refers to a presentation of a sex show or pornographic film which is viewed through a viewing slot.
Your linked first image is seen in the Wikipedia article I linked. It's captioned "Peep show in Golestan Palace"
Raree-show
It may also be called a raree-show, which doesn't come with the negative connotation usually.
In those days both "peep show" and "raree show" were used to mean the same device without it necessarily implying a porn-related meaning.
a small display or scene viewed in a box : peep show; broadly : an unusual or amazing show or spectacle
Your second image is actually from a book cover. "Refashioning Iran - Orientalism, Occidentalism and Historiography. Author: Tavakoli-Targhi M.
So, it was called "peepshow", but now it has a negative connotation, so better to call it "raree-show" now.
I might call it a praxinoscope, although the Farsi term seems to be shahr-e farang. In Hindi the word sandook is used.
From the description and historical timing, it would seem to be some kind of pre-film animation device - see Precursors of Film :: Modern Era on Wikipedia. Look at praxinoscope and zoetrope as well.
The praxinoscope represents a refinement on the zoetrope. The slits are replaced by a set of mirrors that spin in the center of the drum. (the animation book, Kit Laybourne, 1998)
The praxinoscope functions by using rotating mirrors to give the illusion of movement, and the shahr-e farang is an adaptation of that technique.
The praxinoscope is one of several different types of pre-film animation devices involving rotational drums or disks to give the illusion of motion. "Peep shows" and "magic lanterns" of various types predate this specific era, and you've specified that the apparatus came to the King from an exhibition in France, and the presence of the lenses indicates a newer invention; the discovery of the theory of persistence of vision/the thaumatrope in 1824 led to a number of rotational animation devices in the 1930s, including
Strobostrope (Austria)
Phenakistoscope (Belgium)
Zoetrope (Britain)
and following that
"...in 1832 Joseph Plateau created the Anorthoscope and Phenakistiscope; in 1833 Simon Stampler developed the Stroboscope; in 1853, Franz von Uchatius invented the Kinetiscope [sic] which projected moving drawings; in 1861 Samuel Goodale patented a hand-turned stereoscope device which rapidly moves stereo images past a viewer;[8] and in the same year Coleman Sellers II built the Kinematoscope - a series of stereoscopic pictures on glass plates, linked together in a chain, and mounted in a box."
In common usage, I have heard zoetrope used to reference rotational animation devices in general, even though they don't all function the way a "true" zoetrope does.
This design project documented in the Cairo Observer seems to have the best description I can find of the way traditional shahr-e farang function, though therein and elsewhere they are referred to as alternately "peep boxes", "peep show boxes", and "sandook".