Optics Ques 194
Passage Based Questions
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, $n=\frac{c}{v}= \pm \sqrt{\varepsilon _r \mu _r}$, where $c$ is the speed of electromagnetic waves in vacuum, $v$ its speed in the medium, $\varepsilon _r$ and $\mu _r$ are the relative permittivity and permeability of the medium respectively.
In normal materials, both $\varepsilon _r$ and $\mu _r$ are positive, implying positive $n$ for the medium. When both $\varepsilon _r$ 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, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.
(2012)
- Choose the correct statement.
(a) The speed of light in the meta-material is $v=c|n|$
(b) The speed of light in the meta-material is $v=\frac{c}{|n|}$
(c) The speed of light in the meta-material is $v=c$
(d) The wavelength of the light in the meta-material $\left(\lambda _m\right)$ is given by $\lambda _m=\lambda _{\text {air }}|n|$, where $\lambda _{\text {air }}$ is the wavelength of the light in air.
Show Answer
Answer:
Correct Answer: 194.(b)
Solution:
Formula:
Laws of Refraction (at any Refracting Surface):
- Since value of $n$ in meta-material is negative.
$ \therefore \quad v=\frac{c}{|n|} $
BETA
