If you are using Apache HTTPd, you have two options.
Lets say you have copied your front-end and back-end directories as follows:
Back-end (assumed Laravel 5.x) under /var/www/yourappname/api/
Front-end under /var/www/yourappname/frontend/
You can access your app using app.yourdomain.com. (I normally prefer www.yourdomain.com to be a separate server / Apache instance for security and performance reasons).
1. Two sub-domains
Have two sub-domains pointing to same IP address, say app.yourdomain.com for front-end, and api.yourdomain.com for Laravel back-end. Create two virtual hosts in your Apache configuration and document root as follows
For api.yourdomain.com
/var/www/yourappname/api/public
For app.yourdomain.com
/var/www/yourappname/frontend/
Your back-end base URL to be included in front-end app will be api.yourdomain.com/
Advantage: if you wish to split your front-end and back-end on two different Apache instances or separate servers in future, you can do it easily. Also, front-end is static content and hence could be served using other low cost options like S3 based sites.
Caveat: You will have to take care of CORS (https://developer.mozilla.org/en-US/docs/Web/HTTP/CORS) issue. Also, you will need two SSL certificates or multi-domain certificate or wild-card SSL certificate.
I prefer this option and I have used this in one of my setup considering future load.
2. Single Domain and Alias
Set Document Root as
/var/www/yourappname/frontend
Add Alias as follows (http://httpd.apache.org/docs/2.4/mod/mod_alias.html#alias)
Alias "/api/" "/var/www/yourappname/api/public/
Your back-end base URL to be included in front-end app will be app.yourdomain.com/api/
(I have not yet verified this on my setup)
Advantage: You have single domain, and need single SSL certificate.
Caveat: All hits will be on same Apache service and hence difficult to segregate load of compute intensive API requests and static content.
Note: In either case, I have pointed to "public" directory of Laravel framework, to avoid exposing configuration and other directories of Laravel to outside world.