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The electromagnetic waves travel in a medium at a speed of 2.0 × 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:
  • a)
    2.25
  • b)
    4.25
  • c)
    6.25
  • d)
    8.25
Correct answer is option 'A'. Can you explain this answer?
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The electromagnetic waves travel in a medium at a speed of 2.0 ×...
Calculation of Relative Permittivity
To calculate the relative permittivity of the medium, we can use the formula:
\[\text{Speed of light in the medium} = \dfrac{c}{\sqrt{\mu_r \times \epsilon_r}}\]
Where:
- Speed of light in the medium = 2.0 × 10^8 m/s
- Relative permeability (\(\mu_r\)) = 1.0
- Relative permittivity (\(\epsilon_r\)) is what we need to find
- Speed of light in vacuum (c) = 3.0 × 10^8 m/s

Substitute the Values
Substitute the given values into the formula:
\[2.0 \times 10^8 = \dfrac{3.0 \times 10^8}{\sqrt{1.0 \times \epsilon_r}}\]

Solve for Relative Permittivity
Solving for \(\epsilon_r\):
\[\sqrt{1.0 \times \epsilon_r} = \dfrac{3.0 \times 10^8}{2.0 \times 10^8}\]
\[\sqrt{\epsilon_r} = 1.5\]
\[\epsilon_r = 1.5^2\]
\[\epsilon_r = 2.25\]
Therefore, the relative permittivity of the medium is 2.25. So, the correct answer is option 'A'.
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Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring material, then by Snell’slaw,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 /where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and permeability of the medium respectively.In normal materials, both εr and μr , are positive, implying positive n for the medium. When both εr and μr are negative, one must choose the negative root of n. 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 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. Q.Choose the correct statement.

Paragraph for Questions 13 and 14Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurringmaterial, then by Snell’s law, 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, where c is the speed ofelectromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity andpermeability of the medium respectively.In normal materials, both εr and μr, are positive, implying positive n for the medium. When both εr and μrare negative, one must choose the negative root of n. Such negative refractive index materials can nowbe 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 ofpropagation of the refracted light. However, similar to normal materials, the frequency of light remainsunchanged upon refraction even in meta-materials.Q.Choose the correct statement.

Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring material, then by Snell’slaw,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 /where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and permeability of the medium respectively.In normal materials, both εr and μr , are positive, implying positive n for the medium. When both εr and μr are negative, one must choose the negative root of n. 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 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. Q.For light incident from air on a meta-material, the appropriate ray diagram is

Paragraph for Questions 13 and 14Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurringmaterial, then by Snell’s law, 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, where c is the speed ofelectromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity andpermeability of the medium respectively.In normal materials, both εr and μr, are positive, implying positive n for the medium. When both εr and μrare negative, one must choose the negative root of n. Such negative refractive index materials can nowbe 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 ofpropagation of the refracted light. However, similar to normal materials, the frequency of light remainsunchanged upon refraction even in meta-materials.Q.For light incident from air on a meta-material, the appropriate ray diagram is

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The electromagnetic waves travel in a medium at a speed of 2.0 × 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:a)2.25b)4.25c)6.25d)8.25Correct answer is option 'A'. Can you explain this answer?
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