Password Protect Virtual Directory With .htaccess

I have a site with a virtual directory structure like mysite.com/folder/title which is actually a .htaccess rewrite to mysite.com/f/index.php?p=title. I want to password protect the folder folder with .htaccess, and know how to do that with actual folders. But I don’t want to password protect the main site mysite.com, and right now if I put the .htaccess file in the mysite.com directory, I am protecting mysite.com and mysite.com/folder. I have also tried protecting mysite.com/f.

How can I protect only mysite.com/folder using .htaccess?

.htaccess contents of mysite.com.

<IfModule mod_rewrite.c>
RewriteEngine On

RewriteRule ^folder/(.*)$ /f/index.php?p=$1 [PT,L,QSA]
RewriteRule ^folder/*$ /f/index.php [L,QSA]

RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]

</IfModule>

.htaccess file I tried in mysite.com/f This successfully protects the entire site when moved into the other .htaccess file, so I know the path is correct.

AuthName "Restricted Area" 
AuthType Basic 
AuthUserFile /home/myusername/.htpasswd