Rainbow

Raindow is curve is due to the shape of water droplet

As you know the refraction of light is different because different colour has different frequency( or wavelength)

When passing the water droplet, the angles between lights and normal are different.
So rainbow show a curved shape

Prism has a plane surface, the angles between lights and normal are the same

A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines onto droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc, with red on the outside and violet on the inside. More rarely, a double rainbow is seen, which includes a second, fainter arc with colours in the opposite order, that is, with violet on the outside and red on the inside.

Even though a rainbow spans a continuous spectrum of colours, traditionally the full sequence of colours is most commonly cited and remembered as red, orange, yellow, green, blue, indigo and violet.

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude or angle. The most spectacular rainbow displays when half of the sky is still dark with draining clouds and the observer is at a spot with clear sky overhead. The rainbow effect is also commonly seen near waterfalls or fountains. Rainbow fringes can sometimes be seen at the edges of backlit clouds and as vertical bands in distant rain or virga. The effect can also be artificially created by dispersing water droplets into the air during a sunny day.