Does the ammount of daylight increase the same amount each day after the winter solistice?

It varies. Initially, after the winter solstice, the days grow only by a few second. That grows and reaches a maximum daily growth around the equinox. After that the amount of daylight increase begins to decrease, until near the summer solstice, where only a few seconds of additional light are gained.

All this assumes that one is not above the Arctic Circle.

Here is a neat site that can show this: http://akweathercams.faa.gov/srsscalc.php

Just put in your location via latitude and longitude, then change the days and you will see how the length of the days change

As Cyswxman writes, it varies and it does it as a sinusoid. If you don't know what it is, imagine drawing a circle over a piece of paper that moves, you'll end up drawing a wave pattern. That is how the length of the day varies: slowly after the solstice, the bottom and top of the curve, and fastest at the equinoxes, as your drawing pen goes right up or right down.

Here is a funny trivia: Right now, the day is getting slightly longer in the northern hemisphere because we are after the winter solstice (the 21th of Dec). Yet if you check the time of sunset, it is still earlier and earlier. Strange, isn't it?

This is due to what is called the Equation of Time. The orbit of the earth around the sun isn't a perfect circle but an ellipsoid. Because of that, the speed of the earth isn't constant either. As a result the length of a day is only 24 hours as a yearly average. It varies to plus a quarter to minus a quarter, also half an hour, during the course of a year. But, for practical purpose, we keep all our clocks to a day of exactly 24 hours. But it also means that, relative to our clock the sunset is still earlier and earlier until about the 4th of January. Funny, isn't it?

which would be a trick question, and the popular public could go incorrect. in many cases, the equator is meant to be the section the place days are consistently the comparable length. despite the fact that, simply by fact the orbit of the Earth isn't a perfect circle, there will be very tiny ameliorations interior the era of the day.