Trajectory of the light ray in the prism. The ray of light in the prism

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When studying Optics, we saw that a prism is nothing more than a geometric solid made up of three homogeneous and transparent media, basically in the shape of a triangle. We have also seen that when light falls on one face of a prism, it will undergo two refractions.

Therefore, when a polychromatic light (two or more colors) falls on a prism, the phenomenon we know as light scattering, that is, the phenomenon identical to that which forms the Rainbow. The set of colors that make up a polychromatic light is called spectrum from light. The question remains: how does the ray of light behave inside the prism? We will answer this question by knowing the path of the light ray in the prism.

Let's look at the figure above. Let's assume that a prism is immersed inside a transparent and homogeneous medium. For this medium, we will adopt that the material that makes up the prism is more refractive, that is, the refractive index of this medium is greater than the refractive index of the initial medium. We can see that the figure shows us a general scheme of the trajectory adopted by a monochromatic light beam that passes through the prism.

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We can see that the light ray R incident gets to the point I of one of the faces of the prism. Then we can see that this same ray of light R undergoes a refraction. In the scheme, i and r are the angles of incidence and refraction. Right after the first refraction, we see that the light ray propagates through the prism and falls on the other face of the prism exactly at the point I’. Therefore, R’ is the emerging ray, i’ and ha are the angles of incidence and emergence, respectively, of the second face of the prism.

For the trajectory of the light ray in the prism on both sides we can also use the Snell-Descartes equation. Therefore, we have:

Incidence face: n1.sin i = n2.sen r

Emergency face: n2.sen r'=n1.sen i'

By Domitiano Marques
Graduated in Physics

Would you like to reference this text in a school or academic work? Look:

SILVA, Domitiano Correa Marques da. "Trajectory of the light ray in the prism"; Brazil School. Available in: Accessed on June 27, 2021.

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