(a) Identification of Parameters

• Step 1 (Governing Wave Equation): [0.5 Mark]
  The standard equation for a plane electromagnetic wave propagating in the $z$-direction is given by: $$E_x = E_0 \sin(kz - \omega t)$$ Where $k$ is the propagation constant (wave number) and $\omega$ is the angular frequency.
• Step 2 (Relational Analysis): [0.5 Mark]
  (i) The parameter related to wavelength ($\lambda$) is $k$, where $k = \frac{2\pi}{\lambda}$.
  (ii) The parameter related to frequency ($\nu$) is $\omega$, where $\omega = 2\pi\nu$.
• Step 3 (Final Concluded Answer): [0.5 Mark]
  The wavelength is determined by $k$ and the frequency is determined by $\omega$.

(b) Properties of the Medium

• Step 1 (Governing Law): [0.5 Mark]
  The velocity of an electromagnetic wave in a medium is given by the relation: $$v = \frac{1}{\sqrt{\mu\epsilon}}$$ Where $\mu$ is the absolute permeability and $\epsilon$ is the absolute permittivity of the medium.
• Step 2 (Final Concluded Answer): [0.5 Mark]
  The two properties of the medium that determine the velocity of light are:
  1. Permeability ($\mu$): Represents the magnetic property of the medium.
  2. Permittivity ($\epsilon$): Represents the electrical property of the medium.