I want PHP for UI coding and I'm going to be making AJAX demands to some Java after sales. I have never used two servers before. I'll need Apache for PHP and Tomcat for Java.

How do i do that?

You are able to run php through Tomcat because it is according to Apache. This is a really quite simple tutorial to do this. http://nexus.zteo.com/2008/02/15/how-to-setup-php5-with-tomcat-5/

One possibility would be to operate a PHP interpreter designed in Java directly in Tomcat and there's a wide open-source one known as Quercus.

You can run both servers seperately but that will mean, that Tomcat will need to operate on another port. You may also setup PHP with Tomcat like a CGI Script as already pointed out but I'm not sure if that'll provide the best performance.

In my opinion the easiest way would be to connect Tomcat with Apache is by mod_jk conenctor. You just need to tell Apache which pages to redirect towards the Tomcat Server running behind it. Because you did not give more details regarding your system atmosphere I possibly could only provide you with the connect to the overall documentation.