Refractive index is a number that shows how much a material slows down light. When light travels through a coating, it bounces off the front and back surfaces. An optical thickness of one half-wavelength creates a special effect when these waves meet.
The light traveling through the layer and back covers a distance of one full wavelength. This round-trip distance creates a phase shift of one full cycle. Because the shift is a full cycle, the reflected waves line up perfectly with the incoming waves.
This alignment means the layer does not change the overall reflection or transmission of light. For this reason, scientists call it an absentee layer because it acts like it is not there. Students often struggle to understand why we would add a layer that does nothing to the light.
These layers are actually very useful as protective covers on the outside of delicate optics. They can also act as spacer layers inside complex filters without altering the color settings. You can make this thickness by putting two quarter-wave layers next to each other.