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The critical angle of medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will be
  • a)
    60°
  • b)
    45°
  • c)
    15°
  • d)
    30°
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The critical angle of medium for a specific wavelength, if the medium ...
The critical angle of a medium can be calculated using the formula:

sin(critical angle) = 1 / √(n^2 - 1)

where n is the refractive index of the medium. The refractive index can be calculated using the relative permittivity (εr) and relative permeability (μr) using the formula:

n = √(εr * μr)

Given that the relative permittivity (εr) is 3 and the relative permeability (μr) is 4/3, we can calculate the refractive index:

n = √(3 * 4/3)
n = √(4)
n = 2

Now, we can calculate the critical angle:

sin(critical angle) = 1 / √(2^2 - 1)
sin(critical angle) = 1 / √(4 - 1)
sin(critical angle) = 1 / √3

Using a calculator, we can find the value of sin(critical angle) to be approximately 0.577.

Now, we can find the critical angle:

critical angle = sin^(-1)(0.577)
critical angle ≈ 35.3 degrees

Therefore, the correct option is not 60 degrees but approximately 35.3 degrees.
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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.

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The critical angle of medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will bea)60°b)45°c)15°d)30°Correct answer is option 'D'. Can you explain this answer?
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