K-factor in special relativity 
A sends out a series of flashes of light to B, where the interval between flashes is denoted by T according to A's clock. Then it is plausible to assume that the intervals of reception by  B's clock are proportional to T, say KT. (K is the K-factor)
I dont understand this at all. How is it plausible to assume the proportionality of K?
Source : Ray D'Inverno's Relativity Book.
 A: The clock on $A$ is ticking steadily so the interval between each tick, $t_A$, is constant. Since $B$ is moving steadily with respect to $A$ it seems reasonable to suppose that the time interval between the ticks received by $B$ will also be constant. Note that we aren't saying anything about the period of these ticks, just that they are equally spaced so $t_B$ is constant.
So we need some equation to relate $t_B$ to $t_A$, and the question is how to show that:
$$ t_B = K \space t_A $$
for some constant $K$ that will depend on factors like velocity but not on $t_A$.
Given that we know $t_A$ and $t_B$ then we can obviously calculate a value for $K$ because $K = t_B/t_A$. If we use the subscript $0$ to show this is the equation for our reference clock we can write:
$$ t_{B0} = K_0 \space t_{A0} $$
Note that at this stage we aren't claiming this applies to all clocks, only to the clock that ticks with an interval $t_{A0}$.
Now suppose we ignore every second tick sent by $A$. This means we have a clock on $A$ with an interval of $t_{A1}$, where $t_{A1} = 2t_{A0}$. We can work out the interval on $B$ simply by ignoring every second tick on $B$, and we get $t_{B1} = 2t_{B0}$. As above we can write an equation to relate the intervals:
$$ t_{B1} = K_1 \space t_{A1} $$
But we know that $t_{A1} = 2t_{A0}$ and likewise for $t_{B1}$, and if we substitite these values and both sides by $2$ we just get back our first equation. That means $K_1 = K_0$.
Now we can choose only every third tick on $A$ to get a clock running one third as fast, $t_{A2} = 3t_{A0}$, and the same argument will tell us that if we write:
$$ t_{B2} = K_2 \space t_{A2} $$
then $K_2 = K_0$. And so on taking every fourth tick, every fifth tick and so on. For all of these clocks we find that:
$$ t_{B} = K_0 \space t_{A} $$
So, simply by assuming the ticks are received regularly we have shown that $t_B \propto t_A$ for all clocks with frequencies $f$, $f/2$, $f/3$, and so on. So it seems reasonable to suppose this is a general rule and for any clock on $A$ of any frequency we have:
$$ t_{B} = K \space t_{A} $$
For some $K$ that does not depend on $t_A$.
