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Chapter 18: Problem 15

If \(\varepsilon_{0}\) and \(\mu_{0}\) represent the permittivity and permeability of vacuum, \(\varepsilon\) and \(\mu\) represent the permittivity and permeability of medium, then refractive index of the medium is given by (A) \(\sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu \varepsilon}}\) (B) \(\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}\) (C) \(\sqrt{\frac{\varepsilon}{\mu_{0} \varepsilon_{0}}}\) (D) \(\sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu}}\)

Short Answer

Expert verified
The short answer is: The refractive index of the medium is given by option (B) \[n = \sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}\].

Step by step solution

01

Recall the definition of refractive index

Refractive index (n) is the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). It can be written as: \[n = \frac{c}{v}\]
02

Recall the relations between permittivity, permeability, and speed of light

In a medium with permittivity (\(\varepsilon\)) and permeability (\(\mu\)), the speed of light (v) is given by: \[v = \frac{1}{\sqrt{\mu \varepsilon}}\] In vacuum, the speed of light (c) is given by: \[c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\]
03

Substitute the values of c and v in the refractive index formula

Now, substituting the values of c and v in the refractive index formula, we get: \[n = \frac{\frac{1}{\sqrt{\mu_0 \varepsilon_0}}}{\frac{1}{\sqrt{\mu \varepsilon}}}\]
04

Simplify the formula

Simplifying the above equation to find n, we get: \[n = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \times \frac{\sqrt{\mu \varepsilon}}{1}\] \[n = \sqrt{\frac{\mu \varepsilon}{\mu_0 \varepsilon_0}}\] Comparing this to the given options, we can conclude:
05

Choose the correct option

The correct answer is denoted by option (B), which is: \[n = \sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}\]

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Most popular questions from this chapter

In an astronomical telescope, the focal length of objective lens and eyepiece are \(150 \mathrm{~cm}\) and \(6 \mathrm{~cm}\), respectively. In case when final image is formed at least distance of clear vision \((D=25 \mathrm{~cm})\). The magnifying power is (A) 29 (B) 30 (C) 31 (D) 32

A point source of light \(B\) is placed at a distance \(L\) in front of the centre of a mirror of width \(d\) hung vertically on a wall. A man walks in front of the mirror at a distance \(2 L\) from it as shown. The greatest distance over which he can see the image of the light source in the mirror is (A) \(d / 2\) (B) \(d\) (C) \(2 d\) (D) \(3 d\)

The light ray is incident at angle of \(60^{\circ}\) on a prism of angle \(45^{\circ}\). When the light ray falls on the other surface at \(90^{\circ}\), the refractive index of the material of prism \(\mu\) and the angle of deviation \(\delta\) are given by (A) \(\mu=\sqrt{\frac{3}{2}}, \delta=30^{\circ}\) (B) \(\mu=1.5, \delta=15^{\circ}\) (C) \(\mu=\frac{\sqrt{3}}{2}, \delta=30^{\circ}\) (D) \(\mu=\sqrt{\frac{3}{2}}, \delta=15^{\circ}\)

For which of the pairs of \(u\) and \(f\) for a mirror image is smaller in size than the object (A) \(u=-10 \mathrm{~cm}, f=20 \mathrm{~cm}\) (B) \(u=-20 \mathrm{~cm}, f=-30 \mathrm{~cm}\) (C) \(u=-45 \mathrm{~cm}, f=-10 \mathrm{~cm}\) (D) \(u=-60 \mathrm{~cm}, f=30 \mathrm{~cm}\)

A light ray is incident perpendicularly to one face of a \(90^{\circ}\) prism and is totally internally reflected at the glass-air interface. If the angle of reflection is \(45^{\circ}\), we conclude that the refractive index (A) \(n>\frac{1}{\sqrt{2}}\) (B) \(n>\sqrt{2}\) (C) \(n<\frac{1}{\sqrt{2}}\) (D) \(n>\sqrt{2}\)
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