Mime type in nginx for dynamic url

Question

user upload file and its kept in file directory without file extensions

so it looks like file/ID

what i had done, when user download any file, we have created a rewrite rule for the same which looks like

rewrite ^/file/(.+?)/(.*)$ /file/$1;

http://example.com/file/id/name.mp4 -> http://example.com/file/id

now, the problem i face is nginx is giving content-type (mime) a application/octet-stream

Which is not the actual mime type of file, this is because default mime type is application/octet-stream

i also know we can change the same using nginx configuration,

But my question is that can we set mime-type base on the url file extension