91Ó°ÊÓ

Polarization refers to the orientation of the oscillations of the electromagnetic waves. Light waves oscillate in different directions perpendicular to the direction of the wave's travel. In the given problem, the magnetic component of the light wave, denoted as \(B_x\), is oriented along the x-axis. This tells us that the electric field component Must be oscillating in a direction perpendicular to both the magnetic field and the direction of light propagation. Since the light propagates along the y-axis, and considering the perpendicular nature of electric and magnetic fields in electromagnetic waves, the light is polarized along the z-axis.

Frequency is the number of oscillations of a wave that pass a particular point per second. The wave number \(k\) given is \(1.57 \times 10^7 \mathrm{~m^{-1}}\). The wave number is related to the wavelength \(\lambda\) as follows: \[ \lambda = \frac{2 \pi}{k} = \frac{2 \pi}{1.57 \times 10^7 \mathrm{~m^{-1}}} \approx 4.0 \times 10^{-7} \m \] Using the speed of light \(c\) which is approximately \(3 \times 10^8 \mathrm{~m/s}\), we can find the frequency \(f\) using the relationship \[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \mathrm{~m/s}}{4.0 \times 10^{-7} \m} \approx 7.5 \times 10^{14} \mathrm{~Hz} \] So the frequency of the light is \(7.5 \times 10^{14} \mathrm{~Hz}\).

Intensity of light describes the amount of energy a wave carries per unit area per unit of time. To calculate the intensity, we use \( I = \frac{c}{2 \mu_0} E_0^2 \). Here \( E_0\) is the maximum amplitude of the electric field, which can be determined by the relationship between the electric and magnetic fields in light waves: \(E_0 = c B_0 \). Given \( B_0 = 4.0 \times 10^{-6} \mathrm{~T}\) and \( c = 3 \times 10^8 \mathrm{~m/s}\), we get: \[ E_0 = 3 \times 10^8 \mathrm{~m/s} \times 4.0 \times 10^{-6} \,\r{~T} = 1200 \mathrm{~V/m} \] Now substitute \( E_0 \) into the intensity formula: \[ I = \frac{(3 \times 10^8 \mathrm{~m/s})(1200 \mathrm{~V/m})^2}{2 (4\pi \times 10^{-7} \mathrm{~T \cdot m/A})} \approx 1.4 \times 10^3 \mathrm{~W/m^2} \] Therefore, the intensity of the light is approximately \( 1.4 \times 10^{3} \mathrm{~W/m^{2}}\).

Wave number represents the number of wavelengths per unit of distance and is denoted by \(k\). It quantifies the spatial frequency of the wave and is calculated as the reciprocal of the wavelength multiplied by \(2 \pi\): \[ k = \frac{2 \pi}{\lambda} \] In our problem, it is given directly as \( 1.57 \times 10^7 \mathrm{~m^{-1}}\). Understanding the wave number helps in determining various other properties of the wave, such as wavelength and frequency. It is a critical value in analyzing wave interaction with materials and various medium characteristics.

The speed of light in a vacuum is a fundamental constant denoted by \(c\) and is approximately \(3 \times 10^{8} \mathrm{~m/s}\). This value is essential for calculating other properties of electromagnetic waves, including frequency and wavelength, using the relationship \( c = f \lambda \). The speed of light remains constant in a vacuum, but when light travels through different mediums, its speed can change, affecting other properties like refraction.