Understanding Regex Indexing

Working with Data
#1

Hello there,
I have created a schema like this

{
    updated_at:new Date();
    students:[
       {
            section:"B",
            name:"anshul"
       },
       {
            section:"A",
            name:"shubham"
       }
    ]
}

And there are 1 million documents like this with different names (lowercase only) and there must be two elements in the student array.
my query is like this

Students.find(
          {
               students:
               {
                   $elemMatch:
                   {
                     section:"A",
                     name:{$regex:"^s"}
                    }
                }
           }
           ).sort({updated:-1}).limit(20)

I have created a compound index i.e “students.section”:1,“updated”:-1,“students.name”:1

When there are multiple results this index works fine means index scan is low around 20-22
but when I search for specific name or name which are less in collection , all index gets scanned around 1 million.
Could you help me to figure out
how can I maximize the performance and reduce the index scan?