Theory:

Look at the picture below; there are different coloured leaves, aren't they?
 
Leaves_of_different_colours.jpg
Different colours of leaves based on the pigments
 
Do process of photosynthesis occur in colour leaves other than green leaves?
 
Let us test the leaves which are not green in colour, whether they do photosynthesis or not.
 
Steps followed:
  1. Take one or more plants, one with green leaves and the other with different colour leaves.
  2. Remember that the plants undergoing photosynthesis have stored carbohydrates in them.
  3. Performing an iodine test will prove that leaves other than green in colour also have stored carbohydrate in them.
  4. Iodine, in the presence of starch, turns into a blue-black colour.
  5. But if the leaf does not turn blue-black on iodine's addition, then it proves it does not do the photosynthesis.
Observation:
  • Blue-black colour is observed in the green leaf. It indicates the presence of starch.
  • Blue-black colour is not observed in the coloured leaf. It indicates the absence of starch.
starch.png
Presence of starch in different types of leaf
  
Important!
Info box:
Plants containing non-green leaves also exhibits the process of photosynthesis. They have a non-green pigments known as anthocyanins and carotenoids in addition to chlorophylls.
Anthocyanins present in large amount coverup the green pigment chlorophyll.
However, the covered-up chlorophyll continues to perform its function of carrying photosynthesis. Hence colour leaves also involve in the process of photosynthesis. The colour varies from red, orange, and yellow due to carotenoid's presence, which is abundantly found in flowers and fruits.
 
 BeFunky-collage (1).jpg
Fruits and flowers
Reference:
Wikipedia - https://commons.wikimedia.org/wiki/File:Leaves_of_different_colours.jpg