Theory

Cauchy's equation

The refractive index $(n)$ of an optically transparent material depends on the wavelength of the light. The dependence can be written as

$$n=1+A\left(1+\frac{B}{{\lambda }^2}\right)$$

or, $$n-1=A+\frac{AB}{{\lambda }^2}$$

where $A$ is known as coefficient of refraction and $B$ is known as coefficient of dispersion.

Figure 2.1-1: Cauchy's Dispersion Graph

Snell's formula

When the angle of incidence becomes equal to the angle of emergence, i.e. $(i=e)$, deviation becomes minimum $D\to D_{min}$. Also satisfying $i=\frac{A+D_{min}}{2}$ and $t=\frac{A}{2}$.

If angle of the prism $(A)$ is known, then by knowing angle of minimum deviation $(D_{min})$, the refractive index $(n)$ can be found by Snell's formula,

$$n=\frac{sin\left(\frac{A_p+D_{min}}{2}\right)}{sin\left(\frac{A_p}{2}\right)}$$

Where $A_p$ is the angle of prism and $D_{min}$ is the angle of minimum deviation.

Figure 2.1-2: Ray diagram

Dispersive power

$$\omega =\frac{n_B-n_R}{n_Y-1}$$