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JEE Advanced 2012Paper 2
Exam
JEE Advanced
Year
2012
Paper
Paper 2
Subject
Physics
Chapter
Ray Optics

JEE Advanced 2012 · Paper 2 · Physics · Ray Optics

Most materials have the refractive index, n>1 . So, when a light...

Most materials have the refractive index, n>1n>1. So, when a light ray from air enters a naturally occurring material, then by Snell's law, sin⁡θ1sin⁡θ2=n2n1\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=c/v=±εrμr\mathrm{n}=c / v=\pm \sqrt{\varepsilon_{r} \mu_{r}}, where cc is the speed of electromagnetic waves in vacuum, vv its speed in the medium, εr\varepsilon_{r} and μr\mu_{r} are the relative permittivity and permeability of the medium respectively. In normal materials, both εr\varepsilon_{r} and μr\mu_{r}, are positive, implying positive nn for the medium. When both εr\varepsilon_{r} and μr\mu_{r} are negative, one must choose the negative root of nn. Such negative refractive index materials can now be artificially prepared and are called metamaterials. They exhibit significantly different optical behavior, without violating any physical laws. Since nn 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. Question: Choose the correct statement.

Options

  1. AThe speed of light in the meta-material is v=c∣n∣v=c|n|
  2. BThe speed of light in the meta-material is v=c∣n∣v=\frac{c}{|n|}
  3. CThe speed of light in the meta-material is v=cv=c.
  4. DThe wavelength of the light in the meta-material (λm)\left(\lambda_{m}\right) is given by λm=λair ∣n∣\lambda_{m}=\lambda_{\text{air }}|n|, where λair \lambda_{\text{air }} is wavelength of the light in air.

Correct answer

B. The speed of light in the meta-material is v=c∣n∣v=\frac{c}{|n|}

Step-by-step solution

Speed of light in a medium, V=CnV=\frac{C}{n} nn for meta-material =∣n∣=|n| ∴\therefore \quad Speed of light in the meta-material V=C∣n∣V=\frac{C}{|n|}.
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