tip of the nose
Only when written 鼻先
Refers specifically to the physical tip of the nose.
The dog pushed the door with the tip of its nose.
right in front of one; under one's nose
Only when written 鼻先
Used for something happening or placed very close to one's face or immediate vicinity, often with a nuance of surprise or annoyance.
The door was shut right in his face.
The culprit escaped right under the police's nose.
Extended use for the tip or end of a long, narrow object, such as a peninsula or a tool. Less common than the nose-related senses.
A lighthouse stands at the tip of the cape.
The opportunity was right under my nose, but I didn't notice it.
He shut the door right in my face.
The two of them talked so close that their noses almost touched.