What is a formal analysis? A formal analysis is basically a breaking down of an artworks parts in order to understand its whole. If you have read any of my Photo Focus posts, these are basic formal analysis’. However, you can discuss even more parts of the art or photograph than I do. In a formal analysis you can address the artworks source (i.e. the art movement it is a part of or the political issues of the time and place the work was made), the materials it is made of (paper, bronze, ect.), its size, its context (where it is place, example: inside a Jain temple or at a funerary site). Beyond these things, you want to look at the formal elements of the artwork or photograph such as lines, color, texture, shape, form, ect. these are known as the elements and principles of design. Addressing all of these elements will give you an understanding of the artwork.
Photography has some elements that are used more than in other arts like contrast and tonal range in the case of a black and white photograph. Specific to photography are depth of field meaning how much of the photograph is in focus and exposure time. The exposure time determines whether moving subjects are stopped or in motion.
Photography is unique because if you are viewing a reproduction in a book or only, you are typically only seeing the image and not the paper the image is printed on. It is important to note that while a photograph may be considered a two-dimensional object, if printed they are an object with a sliver of dimension. If you are lucky enough to be analyzing a photographic object (the print itself), you can also discuss the size of the paper, is it framed, if not is there anything written or stuck on the back of the photograph, does the paper show wear, has the image faded, has the photograph been torn from an old photo album, has the photograph been written on or defaced in any way and so forth?
Keep in mind that an analysis goes beyond just a description. An analysis is proving a point. What do all of the elements you have discussed say about the art object.