Glassfish and Nginx: same domain for different web apps

Question

I am really a nginx newbie so please excuse the mistakes etc.

The domain: http://www.example.com

The 2 glassfish apps:

http://localhost:8080/app1 http://localhost:8080/app2

What I'd like:

Glassfish app1 served at: http://www.example.com

Glassfish app2 served at: http://www.example.com/app2

At the moment I have:

server {
    listen       80;
   server_name  example.com www.example.com;

    location / {
        proxy_pass      http://localhost:8080/app1/;
        proxy_set_header  X-Real-IP  $remote_addr;
        proxy_pass_header Set-Cookie;
        proxy_pass_header X-Forwarded-For;
        proxy_pass_header Host;    }

    location /app2/ {

        proxy_pass      http://localhost:8080/app2/;
        proxy_set_header  X-Real-IP  $remote_addr;
        proxy_pass_header Set-Cookie;
        proxy_pass_header X-Forwarded-For;
        proxy_pass_header Host;    }
}

But the paths get mixed up. Help?