A Formula for the Scaling Factor of a Constantly Decreasing Image

Date: 9/28/95 at 13:10:29
From: Clifford West
Subject: math

Here's a problem for you:

I'm looking at a picture of a person holding a mirror and looking 
into a mirror.

I see that the image is repeated over and over again.  The large 
picture is made of an infinite number of smaller pictures, all of 
which are proportional.  The first image is about 15cm.  The 
second image is about 5.8cm.  What is the actual height of the 
10th image in the picture?  An explanation as well as a solution 
would be helpful.

Thanks................Clif West  

Date: 10/10/95 at 20:54:30
From: Doctor Jonathan
Subject: Re: math

Sir,

I think that the size of the nth image is given by the expression  
15*(5.8/15)^n where the zeroth image is the original.  The reason 
for this is that each time the image is copied, it is scaled by a 
constant factor of 5.8/15.  Thus, if this process is repeated, the 
total scaling factor is (5.8/15)^n.  The reason the scaling factor 
is constant is that for each iteration, the copied image occupies 
the same portion of the "parent" image.

-Doctor Jonathan,  The Geometry Forum