One thing that having a second smaller sun in the sky does is make the days seem longer. As the two stars orbit their center of gravity in a period of several hours, days, or weeks, sometimes the smaller sun will eclipse the larger one, sometimes the larger sun will eclipse the smaller one, and the majority of the time they will be seen side by side in the sky.
And sometimes as the planet turns only one star will be visible in the sky. James specified that the stars orbit each other at a distance of 0.5 AU. If the planet is at a distance of 1 AU, the stars can look as much as 30 degrees of arc apart in the sky of the planet.
So when the two stars are at their maximum separation, The brighter one will be visible without the dimmer one for about 0.08333 of a planetary rotation period, the dimmer one will be visible without the brighter one for about 0.08333 of a planetary rotation period, and both should be visible together in the sky for about 0.416667 of a planetary rotation period, if my calculations are correct.
Thus when the two suns are farthest apart, the day should last for about 0.58333 of a planetary rotation period and the night last for about 0.41667 of a planetary rotation period. If the planet has no axial tilt, of course.
When the two stars are closer together the periods of only a single sun being visible will be less and less of the total rotation period.
It is possible that the animals and humanoids on James's planet may have adaptations to see better during the light of only one of the two suns.
If James wants to make his system scientifically probable, he should significantly reduce the distance between the two suns. Astronomers have calculated the stability of possible planets in binary systems, including S type orbits, where the planet orbits only one of the stars, and P type or circumbinary orbits where the planet orbits both of the stars.
Wikipedia says:
For a circumbinary planet, orbital stability is guaranteed only if the planet's distance from the stars is significantly greater than star-to-star distance.
The minimum stable star to circumbinary planet separation is about 2-4 times the binary star separation, or orbital period about 3-8 times the binary period. The innermost planets in all the Kepler circumbinary systems have been found orbiting close to this radius. The planets have semi-major axes that lie between 1.09 and 1.46 times this critical radius. The reason could be that migration might become inefficient near the critical radius, leaving planets just outside this radius.[6]
For example, Kepler-47c is a gas giant in the circumbinary habitable zone of the Kepler-47 system.
https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems1
So if James wants to be more scientifically plausible he should move his planet a little bit (but only a little bit or it will be too cold) farther out from the suns and move the suns closer together, or simply move the suns closer together. I would make the suns less than 0.25 AU apart (which is still up to 23,000,000 miles) if the planet is exactly 1 AU from the center of mass of the two suns. Thus the maximum possible separation between the two stars in the sky of the planet would be 15 degrees or less, and there would be less need for the animals to evolve better vision in the light of only one sun.
Another factor is the different frequencies of light emitted by the two suns. Each would emit almost the entire range of electromagnetic radiation from gamma rays to radio waves, but some frequencies would be many times more common than others.
James's original proposal callied for a white dwarf. Most white dwarfs have higher surface temperatures than the sun, some much higher, so their light is the more energetic blue white light. Thus looking at a white dwarf might be more painful than looking at a G type star at the same distance, despite the white dwarf having a much smaller total luminosity.
James modified his question to ask about a red dwarf as the dimmer sun. Red dwarfs have much cooler surface temperatures than G type stars, and the most common frequencies of light they emit are less energetic orangish and reddish frequencies. So if Earth type eyes can handle the yellowish light from G type stars they should have no trouble with the reddish light of red dwarfs, right?
Not exactly.
The Sun has solar flares that are very impressive. If red dwarfs had similar sized stellar flares, they would change the overall luminosity of the red dwarfs much more than solar flares change the overall luminosity of the Sun. Many red dwarfs are flare stars, that have flares many times larger than any solar flare, which make significant changes in the luminosity of the flare stars. The most intense stellar flare recorded may have been up to 10,000 times as strong as any solar flare.
Thus if the red dwarf in the system is a flare star it could easily double the luminosity of the red dwarf for a short time. But since the red dwarf would have only a fraction of the luminosity of the G type star that would not make much of a difference. But the stellar flares of flare stars might often have high energy light rays that might be painful to the eyes of the animals on the planet. Especially when the red dwarf is the only sun in the sky and the eyes have switched to a method of seeing better in the dimmer light of the red dwarf, just as human eyes switch to night vision for seeing in the dark.
Thus it is possible that if the dimmer star is a flare star the animals on the planet might evolve to tolerate occasional intense light from stellar flares, possibly an eyelid or membrane that would instantly shut when detecting intense light, leaving the animal temporarily blind but preventing long term damage to its eyes.
So Jame should decide whether he wants his dimmer star to be a flare star or not and whether he wants the animals and people on his planet to be adapted for occasional flares from the dimmer star.
