Problem When embedding JSON Object inside another object by DBRef

Question

I wrote the code to try DBRef Concept:

The Students Collections has:

{
  "FirstName": "Omar",
  "LastName": "Ali",
  "IsFired": true,
  "FacultyID":
    {
      "$ref": "Faculty",
      "$id": "633d5fca2bed487dd7eb4e11",
      "$db": "FacultySystemV2"
    },
  "CoursesList": [
    {
      "CourseID": {
        "$oid": "633d5fd62bed487dd7eb4e14"
      },
      "Grade": 95
    },
    {
      "CourseID": {
        "$oid": "633d602c2bed487dd7eb4e15"
      },
      "Grade": 80
    }
  ]
}

The Faculty Collections has:

{
  "_id": ObjectId('633d5fca2bed487dd7eb4e11')
  "FacultyName": "Alex University",
  "Address": "Alex City"
}

Unfortunately, it can't recognize the $id or $ref inside the DPRef

var stds6 = db.Students.findOne({"FirstName": "Omar"})
db[stds6.FacultyID.$ref].findOne({"_id": (stds6.FacultyID.$id)})

Even if I write:

stds6.FacultyID.$ref or

stds6.FacultyID.$id I get notinge Faculty Collections has:

{
  "_id": ObjectId('633d5fca2bed487dd7eb4e11')
  "FacultyName": "Alex University",
  "Address": "Alex City"
}

Unfortunately, it can't recognize the $id or $ref inside the DPRef

var stds6 = db.Students.findOne({"FirstName": "Omar"})
db[stds6.FacultyID.$ref].findOne({"_id": (stds6.FacultyID.$id)})

Even if I write:

stds6.FacultyID.$ref

or

stds6.FacultyID.$id

I get noting