Most materials have the refractive index \(n > 1\). So, when a light ray from air enters a naturally occurring material, then by Snell's law, \(\frac{\sin \theta_1 }{\sin \theta_2 } = \frac{n_2}{n_1} \), it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray.
According to electromagnetism, the refractive index of the medium is given by the relation, \(n = \frac{c}{ v} = ± \sqrt{\epsilon_r \mu_r}\), where \(c\) is the speed of electromagnetic waves in vacuum, \(v\) its speed in the medium, \(\epsilon_r\) and \(\mu_r\) are the relative permittivity and permeability of the medium respectively.
In normal materials, both \(\epsilon_r\) and \(\mu_r\) are positive, implying positive \(n\) for the medium. When both \(\epsilon_r\) and \(\mu_r\) are negative, one must choose the negative root of \(n\). Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior, without violating any physical laws. Since \(n\) is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials. For light incident from air on a meta-material, the appropriate ray diagram is

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