A ray of light traveling in air with index of refraction \(n_{\text{air}} \approx 1.0\) strikes the flat top surface of a transparent medium at an angle of incidence \(\theta_0\) relative to the normal. The medium has an index of refraction that decreases linearly with depth \(y\) below the top surface according to \(n(y) = n_0 - \alpha y\), where \(n_0\) and \(\alpha\) are positive constants. As the ray penetrates deeper, it continuously refracts until it travels horizontally at depth \(d\) before turning back toward the top surface. Which of the following is a correct expression for the depth \(d\)?