Question

Why doesn’t any light pass through the filter when the colors of the bulb and filter are different?

Answer 1

Where does the name of the filter come from ?
I mean, why is a red filter called a "red" filter, and why is a "blue" filter
called a "blue" one ?
When you look at a 'red' filter, it looks red. Why do you think that is ?
It's because 'red' light is the ONLY light that can pass THROUGH the
filter and come out of other side. Light of any OTHER color besides red
gets absorbed IN the filter, and never comes OUT the other side.
So, ANY light that passes through the filter and continues to your eye
must be red light ... when you look at the filter, you 'see' red.
But this can only happen IF there's some red light going IN on one side.
If there's no red light going in, then there isn't ANY light coming out, and
the filter looks black !

If the bulb shines with a COLOR, and that color gets ABSORBED
in the filter, then there's no light coming out the other side of the
filter.