Speed of EM Waves in a Medium

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k = 3$ and permeability of $\mu = 2\mu_0$, is ( $\mu_0 =$ permeability of vacuum)

An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, $\varepsilon_r = 9$, has the electric field, $E_x = E_0 \sin\left(kz - 2\pi \times 10^{6} t\right)\text{ V m}^{-1}$ where $E_0$ is the amplitude and $k$ is the wave vector. Among the following options, the incorrect choice is

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t) = 25 \sin\left(2.0 \times 10^{15} t - 10^{7} x\right) \hat{n}$ then the refractive index of the medium is ______. (All given measurement are in SI units)

The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by,

$E_y = 20 \sin\left(3 \times 10^{6} x - 4.5 \times 10^{14} t\right)\text{ V/m}$

(where $x, t$ and other values have S.I. units). The dielectric constant of the medium is ______ (speed of light in free space is $3 \times 10^{8}\text{ m/s}$)

If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by _________ times. $\left(\mu_0 = 4\pi \times 10^{-7}\text{ H/m}, \epsilon_0 = 8.85 \times 10^{-12}\text{ F/m}, c = 3 \times 10^{8}\text{ m/s}\right)$

Electromagnetic waves travel in a medium with speed of $1.5 \times 10^{8}\text{ m s}^{-1}$. The relative permeability of the medium is 2.0. The relative permittivity will be:

If the ratio of relative permeability and relative permittivity of a uniform medium is $1 : 4$. The ratio of the magnitudes of electric field intensity $(E)$ to the magnetic field intensity $(H)$ of an EM wave propagating in that medium is (Given that $\sqrt{\frac{\mu_0}{\varepsilon_0}} = 120\pi$):

Which of the following are true?

A. Speed of light in vacuum is dependent on the direction of propagation.

B. Speed of light in a medium is independent of the wavelength of light.

C. The speed of light is independent of the motion of the source.

D. The speed of light in a medium is independent of intensity.

Choose the correct answer from the options given below:

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x : 1$. The value of $x$ is _________. (Given speed of light in free space $= 3 \times 10^{8}\text{ m s}^{-1}$ and for the given medium $\mu_r = 1$)

An electromagnetic wave, whose wave normal makes an angle of $45^\circ$ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $15^\circ$. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is $3 \times 10^{8}\text{ m/s}$? $\left(\sin 30^\circ = 0.5, \sin 45^\circ = \frac{1}{\sqrt{2}}\right)$

When light propagates through a material medium of relative permittivity $\varepsilon$r and relative permeability $\mu$r, the velocity of light, v is given by (c-velocity of light in vacuum)

Given below are two statements:

Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.

Statement II: In a material medium, the EM wave travels with speed $v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$. In the light of the above statements, choose the correct answer from the options given below.

The electromagnetic waves travel in a medium at a speed of 2.0 $\times$ 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 $\times$ 10 $-$8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?

A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 $\times$ 10$-$2 Am${}^{-1}$ at a point, what will be the approximate magnitude of electric field intensity at that point?

(Given: Permeability of free space $\mu$0 = 4$\pi \times$ 10$-$7 NA${}^{-2}$, speed of light in vacuum c = 3 $\times$ 108 ms${}^{-1}$)

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $-$ 10 $\times$ 1010 t) V/m The velocity of electromagnetic wave in this medium is:

(Given C = speed of light in vacuum)

The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given $\mu$r = 1)

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ____________ $\times$ 107 m/s.

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _________ $\times$ 10$-$2 cm.

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by

E = 20cos(2 $\times$ 1010 t $-$ 200x) V/m. The dielectric constant of the medium is equal to: (Take $\mu$r = 1)

For a transparent medium, relative permeability and permittivity, $\mu_r$ and $\varepsilon_r$ are 1.0 and 1.44 respectively. The velocity of light in this medium would be,

An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:

An EM wave from air enters a medium. The electric fields are

$\vec{E}_1 = E_{01} \hat{x} \cos\left[2\pi\nu \left(\frac{z}{c} - t\right)\right]$ in air and

$\vec{E}_2 = E_{02} \hat{x} \cos\left[k(2z - ct)\right]$ in medium,

where the wave number k and frequency $\nu$ refer to their values in air. The medium is non-magnetic. If $\varepsilon_{r_1}$ and $\varepsilon_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct?

An electromagnetic wave of frequency $\nu = 3.0$ MHz passes from vaccum into a dielectric medium with relative permittivity $\varepsilon_r$ = 4.0. Then

A plane electromagnetic wave in a non-magnetic dielectric medium is given by

$\vec{E} = \vec{E}_0 \sin(4 \times 10^{-7} x - 50t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

The velocity of electromagnetic radiation in a medium of permittivity $\varepsilon$0 and permeability $\mu$0 is given by

An electromagnetic wave of frequency $\nu = 3.0\text{ MHz}$ passes from vacuum into a dielectric medium with permittivity $\epsilon = 4.0.$ Then

If $\varepsilon_0$ and $\mu_0$ are the electric permittivity and magnetic permeability in a free space, $\varepsilon$ and $\mu$ are the corresponding quantities in medium, the index of refraction of the medium is