The headmaster's office and the headmaster's look

Question

Each of these expressions are translated using 'du'.  In English, both are possessive.  In the first case, we are talking about a place, so I can rationalize the use of 'du' instead of 'de'.  In the second case, I have more of a problem.   It seems like a simple use of the possessive which I think would call for 'de' instead of 'du'.  Can I get some guidance here?  Thanks.

Accepted Answer

Frank, the attached link covers this.  
As you note these are both possessive phrases.
When the ‘owner’ in a possessive phrase  ‘de qqn or qqc….’ is described by a noun that is not a proper name, a modifier - definite article in both of these example cases - is required, and contraction occurs between ‘de le’ here to ‘du’.  
https://www.lawlessfrench.com/grammar/possessive-de/ 
This information should be added to the lesson below, as although there is an example ‘de l’enfant’, there is not an explanation of this grammar point and it is not immediately obvious from just one example:
https://progress.lawlessfrench.com/revision/grammar/how-to-express-possession-with-de