You might think that your chances of seeing a rainbow have nothing to do with the time of day. After all, there can be rain, fog or mist followed by a burst of sunshine in the morning, noon or as evening approaches. This is true, yet showers (one of the most common rainbow precursors) are much more frequent in the late afternoon than they are in the early morning or midday, so rainbow sightings are more likely as the day is winding down. The sun is also at a more favorable angle then – 42 degrees or lower in the horizon [sources: Howard, Rao].
We should mention that this phenomenon mainly pertains to rainbows and the summer. In cooler months when the sun doesn't get as high, you might well see a rainbow in midday [source: KOMO News].
Storms typically move from the west to the east, while the sun rises in the east and sets in the west. So if it's raining in the morning, it will likely be raining in the west. Since the sun is in the east, any visible rainbows will be in the west (the sun has to be at your back in order to see a rainbow). In the late afternoon, the situation will be reversed. Now the sun is in the west, and any showers that pop up will hit your locale, then move to the east – the direction you'll need to be looking (with the sun at your back) if you want to spot a rainbow [source: Rao].