Knowing the Angular Deviation

Deflection of light produced by a prism of triangular section

In the study of Optics, we saw that a prism is nothing more than a sheet of non-parallel faces ; the angle formed between the edges is called the opening angle. Therefore, we must study the behavior of a ray of light, which, when crossing the prism, will undergo a deviation, called angular deviation .

The prism has the ability to separate white light, which falls on its face, into different colored beams. We call this set of colored beams, produced by the phenomenon of refraction, the spectrum of white light. This phenomenon is very well observed on rainy days, with the formation of the rainbow.

Let’s look at the illustration above. In it we have a prism immersed in a medium, being traversed by a monochromatic ray – a ray of light formed by a single color, undergoing lateral deviation.

We can see that when the ray of light strikes the left face, that is, the 1st face of the prism, it undergoes the first refraction that can be equated as follows:

Where: 1 is the angle of incidence of the first face and 1 is the angle of refraction of the first face.

Next, we see that the light ray undergoes the second refraction, that is, it undergoes refraction to the 2nd face of the prism, so we have:

2nd   face: n .sen r 2   = n 2 .sen i 2

Where: 2 is the angle of incidence of the second face and 2 is the angle of refraction of the second face.

According to the illustration, we can see that the opening angle (A) is given by:

A = r 1 + r 2

And the angular deviation (Δ m ) can be calculated through the following mathematical relationship:

∆ m =i 1 +i 2 -A

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