A different refractive index. Upon reaching the boundary, the wave is partially reflected and partially transmitted into the second medium. The amount of reflection and transmission depends on the angle of incidence and the refractive indices of the two media.

The behavior of the wave at the boundary can be described using the Fresnel equations, which relate the amplitudes of the reflected and transmitted waves to the angle of incidence and the refractive indices of the two media.

For a wave incident from air onto a dielectric medium, the Fresnel equations are:

\begin{align*}
r_\parallel &= \frac{n_1 \cos \theta_i - n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t} \\
t_\parallel &= \frac{2 n_1 \cos \theta_i}{n_1 \cos \theta_i + n_2 \cos \theta_t} \\
r_\perp &= \frac{n_2 \cos \theta_i - n_1 \cos \theta_t}{n_2 \cos \theta_i + n_1 \cos \theta_t} \\
t_\perp &= \frac{2 n_1 \cos \theta_i}{n_2 \cos \theta_i + n_1 \cos \theta_t}
\end{align*}

where $n_1$ is the refractive index of air (approximately 1), $n_2$ is the refractive index of the second medium, $\theta_i$ is the angle of incidence (measured from the normal to the boundary), and $\theta_t$ is the angle of transmission (also measured from the normal).

$r_\parallel$ and $r_\perp$ are the amplitude reflection coefficients for parallel and perpendicular polarization, respectively, and $t_\parallel$ and $t_\perp$ are the amplitude transmission coefficients. The subscripts indicate the polarization direction relative to the plane of incidence.

The total reflection and transmission coefficients can be calculated by summing the squares of the parallel and perpendicular coefficients:

\begin{align*}
R &= |r_\parallel|^2 + |r_\perp|^2 \\
T &= |t_\parallel|^2 + |t_\perp|^2
\end{align*}

where $R$ is the reflectance (the fraction of incident power that is reflected) and $T$ is the transmittance (the fraction of incident power that is transmitted).

At normal incidence ($\theta_i = 0$), the reflection and transmission coefficients simplify to:

\begin{align*}
r_\parallel &= \frac{n_1 - n_2}{n_1 + n_2} \\
t_\parallel &= \frac{2 n_1}{n_1 + n_2} \\
r_\perp &= \frac{n_2 - n_1}{n_2 + n_1} \\
t_\perp &= \frac{2 n_1}{n_2 + n_1} \\
R &= \frac{(n_1 - n_2)^2}{(n_1 + n_2)^2} \\
T &= \frac{4 n_1 n_2}{(n_1 + n_2)^2}
\end{align*}

In general, the amount of reflection increases as the angle of incidence increases, and is maximum