additional axis, different scale

Dear list,
I am looking for a possibility to present results in a more graphical way by
adding an axis. But I have trouble relating my data to the added axis.
Imagine the following example:

a<- c(10, 20, 30, 40)
b<- c(50, 250, 500, 600)
ba<- b/a

par(las=1, mar=c(5,5,.5,5))
plot(a,b,     type="b", pch=22, cex=2, col=4, lwd=2, ylim=c(0,650),
xlim=c(0,45))
   axis(4, at=c(seq(0,600,length=6)), lab=c(seq(0,25,length=6)), col.axis=2 )
   lines(a,ba, type="b", pch=21, cex=2, col=2, lwd=2, lty=1)

I want the red line to relate its values to the x-axis (a) and axis 4 (on
the right) and not as usual to the x-axis (a) and the y-axis (b).
This would show the tendency of the red line much clearer which now can't be
seen because of the very different scaling.
E.g. I want R to know that I am trying to plot the first point of the red
line P1(50/5) using the x-axis and the right axis, not the y-axis on the
left ect.

I would like to solve this without using a factor solution like:
   bb<-600/25 * ba
   lines(a,bb, type="b", pch=21, cex=2, col=3, lwd=2, lty=1)