to deepen
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to become absorbed in
To engage with something intensely and with concentration, so that one forgets one's surroundings.
Er vertiefte sich so in das Buch, dass er die Zeit völlig vergaß.
He became so absorbed in the book that he completely forgot the time.
The verb 'vertiefen' (to deepen) is derived from the adjective 'tief' (deep). The prefix 'ver-' turns it into a verb that means 'to make deeper' or 'to make more intensive'. It is an inseparable verb.
Wir sollten dieses Thema in der nächsten Sitzung vertiefen.
We should deepen this topic in the next meeting.
The grammar helps with distinguishing the meanings: The reflexive form 'sich vertiefen in' (to become absorbed in) always means 'to concentrate'. The transitive form (with an accusative object) refers either to abstract things like knowledge and relationships or to physical objects like a pit.
Sie vertiefte sich in ihre Arbeit und bemerkte nicht, wie spät es wurde.
She became absorbed in her work and did not notice how late it had become.
This meaning is always reflexive and is used with the preposition 'in' followed by the accusative. The structure is: 'sich in etwas (Akk.) vertiefen' (to become absorbed in something).
Am Wochenende vertiefe ich mich gerne in einen guten Roman.
On weekends, I like to become absorbed in a good novel.
In the abstract meaning, 'vertiefen' (to deepen) is often combined with positive concepts. Typical objects are: knowledge, knowledge/understanding, a friendship, the relationship, or the understanding.
Durch die Reise konnten wir unsere Freundschaft weiter vertiefen.
Through the trip, we were able to deepen our friendship further.
to strengthen / reinforce / amplify
'verstärken' and 'vertiefen' can both express that something becomes more intense. 'verstärken' is used when something gets more force, effect, or strength. This can fit with feelings, sounds, problems, or measures. 'vertiefen' is used more when something becomes more thorough or closer, for example knowledge, skills, or a relationship. The words can be confused because both describe an increase. But 'verstärken' means more strength, while 'vertiefen' means more depth or more understanding. You strengthen an effect, but you deepen knowledge.
Im Kurs vertieft Mehmet seine Kenntnisse in Grammatik.
In the course, Mehmet deepens his knowledge of grammar.
Das viele Üben verstärkt ihr Selbstvertrauen vor der Prüfung.
All the practice strengthens her confidence before the exam.