How can Sinatra be configured to run within a virtual sub-directory of a reverse proxy?

I have an app in Sinatra that accepts requests at the root and with a name using:

get '/'
  'Root page'
end

get '/:name'
  #Some code here
end

When hosting the application behind a reverse-proxy using a sub-directory (i.e. http://some.thing/news points to http://localhost:4567/ ), I want to have /news to go to the get '/' route and /news/old to go to the get '/:name' route.

What configuration does Sinatra need for it to know that it's hosted within a virtual directory and not at the root of the domain? Is this even possible?

The environment within which the application is deployed uses Apache as a reverse-proxy. To re-create the scenario for a quick test, I set up nginx on my computer with:

location /news {
  proxy_pass http://localhost:4567;
}

Going to /news causes it to go to the /:name route instead of the / route.

Solution

Instead of trying to approach the problem from the framework, we can solve the problem from the reverse-proxy.

Nginx has the ability to rewrite the URL. For example:

location /news { 
  rewrite /news(.*) /$1 break;
  proxy_pass http://localhost:4567;
}

Apache does not need any configuration apart from defining the ProxyPass directive. Here's me entire httpd.conf file:

ServerRoot "/opt/homebrew/opt/httpd"
Listen 127.0.0.1:1082 
ServerName Nitins-MacBook

LoadModule mpm_prefork_module lib/httpd/modules/mod_mpm_prefork.so
LoadModule log_config_module lib/httpd/modules/mod_log_config.so
LoadModule unixd_module lib/httpd/modules/mod_unixd.so 
LoadModule authz_core_module lib/httpd/modules/mod_authz_core.so

LoadModule mime_module lib/httpd/modules/mod_mime.so 
AddType text/html .html

DocumentRoot "/Users/nitin.katkam/Documents/practice/frabjous/"
CustomLog "/Users/nitin.katkam/Documents/practice/omniauthgh/httpd_log" common
ErrorLog "/Users/nitin.katkam/Documents/practice/omniauthgh/httpd_err_log"

LoadModule proxy_module lib/httpd/modules/mod_proxy.so 
LoadModule proxy_http_module lib/httpd/modules/mod_proxy_http.so 

<Location "/snow"> 
  ProxyPass "http://localhost:3000"
</Location>

Absolute URLs within the HTML are not automatically re-written and may need more configuration settings.