# Deviation of light by a prism

PDFA prism of angle at the apex *A *and index *n – the *air, of unit index, surrounds the prism – deflects a light beam, whose angle of incidence on one of the lateral surfaces of the prism is *i*, according to the laws of Snell-Descartes of geometric optics: sin *i* = *n* sin *r* and *n* sin *r’* = sin *i’* (Figure 1 for the notations). The angle of deflection *D* = *i* + *i’* – *A*, with *A* = *r* + *r’*.

The light beam can only emerge from the prism if *A < *2 a sin(1/n)* ;* for ice n = 1.31, hence A < 99.5⁰. If we trace the deviation *D* as a function of *i*, we see that it decreases rapidly, reaches a minimum *minimorum* corresponding to a symmetrical crossing of the prism* (i* = *i’*), then increases slowly. The minimum is very flattened, so that a change in the angle of incidence around the incidence that corresponds to this minimum does not significantly change its value; it results in an accumulation of light and therefore a high luminosity around this minimum. For *A* = 60⁰, the minimum is 22⁰; if *A* = 90⁰, it is 46⁰ (Figure 2). Figure 3 shows the value of this minimum for the different values of *A* allowed: it increases with *A*.

In addition, since the index *n *depends on the colour of the incident radiation, the minimum also depends on it; a prism breaks down white light into its various monochromatic components. This explains the iridescence of halos obtained by refraction. For *A* = 60⁰, we have a minimum close to 22⁰ that grows from red to blue (Figure 4).

#### References and notes

**Cover image. **[Source: iwannt via VisualHunt.com / CC BY]