test@dcrosta> db.foo.find()
{ "_id" : ObjectId("4ec67287f4c2536f2b40c43a"), "i" : 0, "len" : 0, "arr" : [ ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c43b"), "i" : 1, "len" : 1, "arr" : [ 0 ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c43c"), "i" : 2, "len" : 2, "arr" : [ 0, 1 ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c43d"), "i" : 3, "len" : 0, "arr" : [ ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c43e"), "i" : 4, "len" : 1, "arr" : [ 0 ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c43f"), "i" : 5, "len" : 2, "arr" : [ 0, 1 ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c440"), "i" : 6, "len" : 0, "arr" : [ ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c441"), "i" : 7, "len" : 1, "arr" : [ 0 ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c442"), "i" : 8, "len" : 2, "arr" : [ 0, 1 ] }
{ "_id" : ObjectId("4ec67287f4c2536f2b40c443"), "i" : 9, "len" : 0, "arr" : [ ] }
test@dcrosta> db.foo.createIndex({len: 1})
test@dcrosta> db.foo.find({arr: {$in: [1]}, len: 2}).explain()
{
  "cursor" : "BtreeCursor len_1",
  "nscanned" : 3,
  "nscannedObjects" : 3,
  "n" : 3,
  "millis" : 0,
  "nYields" : 0,
  "nChunkSkips" : 0,
  "isMultiKey" : false,
  "indexOnly" : false,
  "indexBounds" : {
    "len" : [
      [
        2,
        2
      ]
    ]
  }
}
test@dcrosta> db.foo.find({arr: {$in: []}, len: 2}).explain()
{
  "cursor" : "BasicCursor",
  "nscanned" : 0,
  "nscannedObjects" : 0,
  "n" : 0,
  "millis" : 0,
  "nYields" : 0,
  "nChunkSkips" : 0,
  "isMultiKey" : false,
  "indexOnly" : false,
  "indexBounds" : {
    
  }
}