What makes index size reduction of an index on embedded field in an array

Which data structure is adopted by index on embedded field in an array that reduce index size ?
For example, consider two collections i) Denormalized collection ‘DN’ , and ii) Embedded collection ‘Emb’. Index size of an index on arr.rootfield1 in an embedded collection is less than index on rootfield1.
DN: { id: , rootfield1 : , rootfield2 : }
Emb : { id: , arr : [ {rootfield1:, rootfield2:} ,
{rootfield1:, rootfield2:} ] }