Let’s start by making one thing clear: There are no animals that “need” light in the way that photosynthetic organisms do. Only plants and certain microbes are capable of performing photosynthesis (“photosynthetic” corals and clams, don’t need light, their endosymbiotic dinoflagellates do).
So, no, copepods don’t absolutely require light for their survival. However, that doesn’t mean that they can just “take it or leave it.” Like so many animals, light (or its absence) plays a strong role in their diurnal (i.e. day-to-day) and reproductive behavior. For example, though many pods must venture into the shallow sunlit zones (where the algae are) to feed, they only do so at night when they can more easily evade their predators. During the day, these negatively phototactic (i.e. light-avoiding) species retreat to the deep in oceanic habitats or hide in shadows in shallow nearshore habitats.
If copepods require lighting at all, whether in Nature or in captive systems, it is for their nutritional health. While they eat a rather wide variety of food items (even nutritionally poor material like detritus),
they require certain amounts of algae in their diet. This is because they cannot synthesize important nutritional components (e.g. vitamin C and certain fatty acids) and therefore must obtain them through the things they eat. Copepods fulfill their daily needs for these substances by eating algae!
Algae, of course, require light to survive. And most aquaria (certainly reef aquaria) receive sufficient light to support algae growth, both desired and undesirable. And because few aquarists maintain aquaria without fish--which release copious nutrients such as ammonia and phosphate--there is usually plenty of algae fertilizer around. Combining light and fertilizer in the presence of algae only leads to algal blooms!
These blooms are bad for both the appearance and health of the aquarium ecosystem. That is why aquarists so often employ copepods to naturally control them. A population of aquarium pods can last so long as (1) their planktonic larvae have plenty of phytoplankton to eat and (2) the adults have plenty of benthic film algae to eat.
Copepods can indeed survive without light, but they nevertheless still require algae in their diet! Thus, if raised in total darkness, copepods need to be fed a high-quality, nutritionally balanced, algae-based diet such as OceanMagik.
If you are wondering if copepods need light or not because you want to know if you should put a light on your refugium or not, you 100% need light on your refugium if you want to get the most out of it. It's understandable why you may not want to buy another light. Aquarium equipment, especially reef aquarium equipment, is expensive. Some refugium lights can be as much as $450. For some, those lights are worth and it and needed. For others, that's just unreasonable. There are other lights such as this Kessil H80
that are $129. Another option is the $80 ChaetoMax refugium light from Innovative Marine
Why do you need special lighting for your refugium? As we established, the copepods don't need special lighting themselves. However, refugiums are often used to grow macroalgae. Macroalgae is great for your aquarium because it competes with nuisance algae by consuming nutrients in the water. For macroalgae to work the best it can, it needs to be receiving a higher amount of light than your display.
Why does this matter for your copepods? It doesn't really. If you want to have a refugium just for copepods, then you can probably get away with a cheap light as long as it can grow some algae. However, if you have a refugium, why not utilize it more by growing macroalgae in it? That's what makes refugium so awesome; they can serve multiple purposes at once. Likewise, a refugium light will grow macroalgae to remove nutrients, provide light so that the copepods perform their normal reproductive behavior, and it will grow microalgae for the copepods to eat.
If you are culturing copepods outside of your aquarium, you probably don't need to invest in a refugium light. However, most hobbyists are concerned with keeping copepods in their refugiums or elsewhere in their aquarium system.
So, do copepods need light? No, they absolutely don't need light. Should you give them light? Defineltey, for the reasons we talked about. Should you add a proper refugium light to your refugium? One thousand percent yes!