working of index in join query

My question is regarding the

output. Please refer the below query and its

command output

Explain 
update 
test.table1 t1 
join test.table2 t2 
on t1.field1=t2.field1
and t1.field2=t2.field2
set  t2.field3=t1.field3;

Below is the result of the EXPLAIN command. I added a composite index on (

,

) to both

and

, and then executed the query. After adding the index, the query performance improved significantly. Based on the output of the

command, I confirmed that the query is properly utilizing the index. However, I have a question regarding the details of the

output. Specifically, there is no indication of index usage for

. In the

output (please refer to the image), the

field for

is shown as NULL. Does this mean that the index on

is not being used? If so, how is the query executing so quickly? In other words, if no index is used on

, what mechanism is allowing the matching process in

to perform so efficiently? I am using MySQL 8.0.42