Zaid Alsalami, Shaykh Dr Zaid Alsalami is an Iraqi born scholar, raised in Australia. He obtained a BA from Al-Mustafa University, Qom, and an MA from the Islamic College in London. He also obtained a PhD from... Answered 2 months ago

Bismihi ta'ala

The only place that becomes najis is where the contact occurred. So, if it was the tip of your finger, then that is the place that should be washed.

Unless the tip of your finger becomes najis, and is soaking wet, and you raise your hand up, allowing the water to run down your arm, in which case you will need to wash that area. 

And Allah knows best.