Not quite. Your image tag will still need to point to the 'visible' server, but the server will be able to decode the URL and proxy the request to the proper server.

One way to do this is to use the ProxyPass directive provided by mod_proxy. Put something like the following in the conf file for the visible server:

ProxyPass /10_50_1_1/ http://10.50.1.1/
[download]

Now an URL pointing to http://visibleserver/10_50_1_1/foo/bar would get proxied by the server to http://10.50.1.1/foo/bar. Of course you could use another string in place of 10_50_1_1 to make your URLs look nicer.

If you need more control over how the URL gets rewritten, have a look at the mod_rewrite module, which will work in concert with the mod_proxy module.

ps. if you do setup mod_proxy, make sure you do not set it up as an open proxy... Make sure you have 'ProxyRequests off' somewhere in your config file. The ProxyPass directive will still work regardless of this setting.