Binoculars are telescopes.
Telescopes are used to view distant objects. They consist of a long tube with a big convex lens called (objective lens) towards the objects and a small convex lens called eye piece. The ratio of focal length of objective to that of eye piece gives us the magnification. The image appears inverted when we view it. Length of telescope is the sum of focal lengths of two lenses.
To make the image erect (not inverted) for our eye, we need to add another inverting lens in the middle of the two lenses. This increases the length of the telescope by 4 times the length of this inverting lens.
For obtaining a good view of distant objects, the size of telescope has to be very big in diameter and in length too. They are heavy and cannot be conveniently handled.
Prismatic telescopes solve this problem by use of two triangular prisms to invert the image between the eye piece lens and the objective lens. The first prism receives parallel rays from distant objects and reflects (total internal reflection) rays on to another prism which totally internally reflects rays back towards the eye piece. These rays are now viewed through eye piece with a large magnification.
The structure of binoculars changes due to prisms. The objective and eye piece are not aligned. There is a bulge in between them to accommodate the prisms. Binoculars becomes a bit heavy but its length is short as compared to a telescope.
The incoming rays from the objects fall on prism 1, get reflected twice, and again get reflected twice in the 2nd prism. So the total length of telescope is reduced by the reflections. But the rays travel the same distance (optical path) in a telescope of binoculars.
The prism is made of a highly dense (optical) glass and has a high refractive index. So the critical angle is small. For small angles of incidence the light is totally reflected.
When the two objective lenses, one for each eye, are separated by a large distance then the 3-d effect is more pronounced for the viewer.
Each plastic tube corresponding to each eye has the structure as shown in figure.
The objects look bright because the light is totally reflected.
To design the product :
you need to decide the magnification, diameter (or focal length) of objective and eye piece.
Then total path length of light inside binoculars is = sum of these two focal lengths.