Question #43192

A monochromatic plane light wave of constant frequency $f_0$ is continuously incident from vacuum ($z < 0$) onto a non-magnetic dielectric medium ($z > 0$) at an angle of incidence $\theta_i = 60^\circ$. The boundary at $z=0$ is stationary. The refractive index of the medium is spatially uniform everywhere in $z > 0$, but varies slowly with time as $n(t) = n_0 (1 + \alpha t)$, where $n_0 = \sqrt{3}$ and $\alpha > 0$.

Consider a specific, short wave packet that crosses the boundary into the medium at $t = 0$. At a later time $t = t_1$, the refractive index of the entire medium has become $n(t_1) = 2\sqrt{3}$. Let $f_1$ be the instantaneous frequency of this specific wave packet at $t = t_1$, and $\theta_1$ be the angle its wave vector makes with the z-axis at $t = t_1$. Assume the medium remains isotropic and dispersionless. Which of the following is correct?