Solution (source code)

= Solution

The traditional <infrared photometric bands> extending the optical <photometric system> into this range are approximately
$$
\boxed{J:1.25\,\mu{\rm m},\quad H:1.65\,\mu{\rm m},\quad K:2.2\,\mu{\rm m},\quad L:3.5\,\mu{\rm m},\quad M:4.8\,\mu{\rm m}.}
$$
Their <photometric passbands> lie mainly in <atmospheric windows> between strong molecular absorption bands. This makes ground-based observations practical. The exact centers depend on the system: $L'$ is near $3.8\,\mu{\rm m}$, and shortened $K_s$ and $M'$ bands reduce unwanted background or absorption. At the longest wavelengths, atmospheric and instrumental <thermal radiation> make <sky brightness> especially important. A modern $Y$ band near $1.0\,\mu{\rm m}$ is an additional choice, rather than one of the traditional $JHKLM$ extensions.