Question

why only seven colour occurs in a rainbow

Answer 1

Here is your answer mate:
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Rainbows appear in seven colors because water droplets break white sunlight into the seven colors of the spectrum (red, orange, yellow, green, blue, indigo, violet). You can only see a rainbow if the Sun is behind you and the rain in front.
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Answer 2

Rainbows: Refraction of the Seven Colors of the Spectrum. A rainbow hasseven colors because water droplets in the atmosphere break sunlight intoseven colors. A prism similarly divides light into seven colors. When light leaves one medium and enters another, the light changes its propagation direction and bends.
Hope this helps u mate.
Thanks