Question

give reason why the period of twilight and dawn increase polewards

Answer 1

First, we need to define twilight. There are three, Civil, maritime and astronomical. Each is determined by how far below the horizon the sun is. For civil it is 0 to 6 degrees, maritime 6 to 12 degrees and astronomical 12 to 18 degrees. 
If we start on June 21st the earths pole is tilted 23 degrees towards the sun. Latitudes greater than 67 degrees are in 24 hour daylight on this day. For latitude 61 degrees it will be in civilian twilight from sunset to sunrise Jumping to 49 degrees north there is no period of total darkness after the sun sets. As you move further south, periods of twilight diminish. 
The periods of twilight increase as you move northward only between the spring and autumnal equinoxes. From the autumnal to spring equinoxes, the opposite is true.

Answer 2

The period of twilight increases at the poles as the period during which the refracted light is received at the Equator is short as the sun rises and sets in a vertical path there.