Step 1: Write Snell's law for the two media.
\[ n_1 \sin\theta_1 = n_2 \sin\theta_2 \] with medium 1 denser, so \(n_1 > n_2\).
Step 2: Rearrange to compare the angles.
\[ \sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 \] and since \(n_1/n_2 > 1\), it follows that \(\sin\theta_2 > \sin\theta_1\), which means \(\theta_2 > \theta_1\).
Step 3: Translate the angle comparison into bending direction.
The refracted ray makes a bigger angle with the normal than the incident ray did, so as the light leaves the denser medium and enters the rarer one it swings farther from the normal line, not closer to it.
\[ \boxed{\text{Bends away from the normal}} \]