I recently took the panorama photo of a rainbow below using my iPod (you can see that some part of the rainbow has faided). I would like to somehow enhance the colors of the rainbow to make it more vibrant. Is there any way to go about doing that?
2 Correct answers
Convert to Lab Color. Curves with a 10x10 grid and scale highlight end in the lower left corner.
Duplicate the layer.
Rotate the a and the b curves 4 boxes counterclockwise to increase saturation. Straight-line Curve. The center point must not move. Colors will scream with saturation.
Important: Gaussian blur to soften the rainbow. Reduce Layer opacity slightly.
Add a mask and with a soft brush bring back the non-rainbow area
Reduce the opacity of the rainbow a bit more to keep the rainbow-red from
...
Theoretically one could go into Camera Raw, use the adjustment brush to highlight the rainbow and then edit it... see example below. That was just done quickly... one could be more precise. 
Regardless the way.... it is fun to toy around with a picture and see all the different solutions offered.
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Convert to Lab Color. Curves with a 10x10 grid and scale highlight end in the lower left corner.
Duplicate the layer.
Rotate the a and the b curves 4 boxes counterclockwise to increase saturation. Straight-line Curve. The center point must not move. Colors will scream with saturation.
Important: Gaussian blur to soften the rainbow. Reduce Layer opacity slightly.
Add a mask and with a soft brush bring back the non-rainbow area
Reduce the opacity of the rainbow a bit more to keep the rainbow-red from appearing too intense
Change mode back to RGB
A somewhat similar effect can be obtained in RGB via Image > Adjustments > Hue/Saturation: duplicate layer, over saturation, blur and masking.
There is always a million ways to do things in Photoshop.
I used the CAMERA RAW filter to quickly edit the photo.
I felt the buildings were too dark at the bottom, so I fixed that. Then I decided to make the sky a little less dismal and gave it a little blue.
With Camera Raw you can really experiment and come up with hundreds of ways to edit the photo.
Theoretically one could go into Camera Raw, use the adjustment brush to highlight the rainbow and then edit it... see example below. That was just done quickly... one could be more precise. 
Regardless the way.... it is fun to toy around with a picture and see all the different solutions offered.
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