Question

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, $\dfrac{\sin {{\theta }_{1}}}{\sin {{\theta }_{2}}}=\dfrac{{{n}_{1}}}{{{n}_{2}}}$, 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, $n=\dfrac{c}{v}$, where c is the speed of the electromagnetic waves in vacuum, $v$ its speed in the medium, ${{\varepsilon }_{r}}$ 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 behaviour, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, like normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.
Answer the following:
A) speed of light in meta-material is $v=c\left| n \right|$
B) speed of light in meta-material is $v=\dfrac{c}{\left| n \right|}$
C) speed of light in meta material is v=c
D) None.

Answer 1

Use the above information given to find the speed of light in metamaterial. As the metamaterials refractive index is negative, we must use the mathematical quantity modulus. The speed of light in meta-material is given as the ratio between the speed of light and the refractive index.

Complete answer:
From the above information, we can write down the speed of light in metamaterial as $v=\dfrac{c}{n}$. The above content tells us that there are materials with some negative refractive index, and they are possible to create now.
As the refractive index of the meta-material is negative, we must add modulus to write the speed of light in meta-material because the speed cannot be negative. It can only be zero or positive.
Therefore, the speed formula of light in meta-material is written as,
$v=\dfrac{c}{\left| n \right|}$

Therefore, the correct option is option b.

Additional information:
The metamaterial is any material engineered to have a property that is not found in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics materials are usually arranged in repeating patterns materials derive their properties not from the properties of the base materials, but from their newly designed structures their precise shape geometry size and arrangement gives them their small smart properties capable of manipulating electromagnetic waves hey. They block absorb the enhancement and they bend waves to achieve benefits that go beyond what is possible with conventional materials. In bulk materials, they are appropriately designed so that they affect waves of electromagnetic radiation. There are many applications of metamaterials, and they are diverse in nature. One of the top applications include optical filters, medical devices, remote aerospace applications and sensor detection.

Note:
The speed of any object can never be negative. In the above case if the refractive index of the metamaterial is negative when we put it in the speed of the light in metamaterial formula the speed we get is negative. In order to get out of this situation, we use the modulus symbol so that the velocity of the light in the metamaterial will not be negative.