The raindrops are acting like prisms but, also, the light bounces off the inside of the droplets: that’s how the light comes back at us. With the primary rainbow, the light is bent a total of about 139° whereas for the secondary rainbow it bounces twice for a total angle of around 231°. Because the secondary rainbow’s angle is more than 180°, the light crosses over itself, causing the colours to appear reversed.
Here’s [a diagram](https://www.daviddarling.info/images/rainbow_physics.jpg) that shows what’s going on.
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