Question

a paragraph on why prisms are used in binoculars

Answer 1

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.

Answer 2

    Binoculars have two lenses usually either both biconvex or one biconvex and one biconcave.  The length of the (binoculars or telescope) is the sum of focal lengths of the two lenses.  The images appear inverted through the binocular.  But for viewing a game or observing a distant object on Earth, we want to see upright images.

   So we want to another lens in between the two lenses to make the image upright.  The length of the telescope will be increased a lot (4 times the focal length of the inverting lens).  

  In order to overcome this, and the heaviness of the lenses and the lens holding tubes, we use prisms with small critical angles and high refractive indices.  We introduce one prism to reflect (total internal reflection) rays from the objective lens.  The rays are further reflected (total internal reflection) towards the eye piece.  The prisms are kept a little tilted to the incoming rays.   The shape of the path of the rays will be like  a "Z".

    In a binoculars, there are two objective lenses.  There are four prisms.  Then there are two eye piece lenses.  There are more advantages in terms of weight, clarity, brightness of image, commercial advantage, compactness.  The binoculars instead of being two parallel tubes, becomes bulged in the middle.