1: Isn't exactly infinite series if there are just 2 panes.

If you let the intensity of incident light be 400

1/4th is transmitted from pane 1, or intensity of transmitted is 100

This 100 intensity light is now the incident on second pane.

Again 1/4 th is transmitted so the final intensity is 100/4 =25

in general it's going to be (x/4)^n where x is intensity of initial ray and n is the number of panes.

2: You are walking at a speed of 1m/s and the rope is supposedly lengthening by 1000m/s

so say you are able to cross it after 't' seconds.

that would be possible if

(t)*(1 m/s) = 1000+[(1000m/s)*(t)] (since initial length of ope is 1000m and it is lengthening by 1000m/s)

which fives a t<0, which is not possible.

Hence you can not cross it even if you were God.