Thread: Worded infinite series problem

Hi I was wondering if I could receive some help on a couple of worded infinite series problems:
1. A pane of a certain type of glass reflects half the incident light, absorbs one-forth, and transmits one fourth. A window is made of two panes of this glass separated by a small space. What fraction of the incident light I is transmitted by the double window?

2. Imagine a very thick, one kilometre long tightrope made from rubber. You start at one end and walk along the rope at 1 meter per second. At the end of each second, the rope is stretched, so that it is one kilometre longer than before. You are are carried along with the stretching. Assuming that you are immortal and can keep on walking forever, the rope never breaks, etc., will you ever reach the end of the rope?

Thanks

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.

For 2, see Ant on a rubber rope.