Explain the phenomenon of atmospheric refraction and calculate the time difference between actual and apparent sunset due to this effect.

The Earth rotates $360^\circ$ in 24 hours.
So, the rotation rate is $\frac{360^\circ}{24 \text{ hours}} = 15^\circ \text{ per hour}$.

$15^\circ \text{ per hour} = \frac{15^\circ}{60 \text{ minutes}} = \frac{1^\circ}{4 \text{ minutes}}$.
This means the Earth rotates $1^\circ$ in 4 minutes.

The apparent shift in the sun's position due to atmospheric refraction at the horizon is approximately $0.5^\circ$.
Time difference $= 0.5^\circ \times \frac{4 \text{ minutes}}{1^\circ} = 2 \text{ minutes}$.

Therefore, the time difference between actual sunset and apparent sunset is about 2 minutes.

The correct option is (B).
The time difference between actual sunset and apparent sunset is about $\boxed{\text{2 minutes}}$.