My team is trying to setup an Apache reverse proxy from a customer\'s site into one of our web applications.
http://www.example.com/app1/some-path maps to http://intern
The AskApache article is quite helpful, but in practice I found a combination of Rewrite rules and ProxyPassReverse to be more flexible. So in your case I'd do something like this:
ServerName www.example.com
ProxyPassReverse /app1/some-path/ http://internal1.example.com/some-path/
RewriteEngine On
RewriteRule /app1/(.*) http://internal1.example.com/some-path$1 [P]
...
I like this better because it gives you finer-grained control over the paths you're proxying for the internal server. In our case we wanted to expose only part of third-party application. Note that this doesn't address hard-coded links in HTML, which the AskApache article covers.
Also, note that you can have multiple ProxyPassReverse lines:
ProxyPassReverse / http://internal1.example.com/some-path
ProxyPassReverse / http://internal2.example.com/some-path
I mention this only because another third-party app we were proxying was sending out redirects that didn't include their internal host name, just a different port.
As a final note, keep in mind that Firebug is extremely useful when debugging the redirects.