1. Why are some substances coloured?

2. Why?
There are many reasons why substances appear coloured but for most physical materials it is because the absorption and/or scattering properties of the material are different for different wavelengths of light.
So a substance that appears yellow may do so because it absorbs most strongly in the blue part of the spectrum and scatters most strongly in the red and green parts of the spectrum.
It is often the case that a pigment scatters light most efficiently in one region of the spectrum whilst having its main absorption band in another.
This explains why translucent and transparent coloured films can have different hues when viewed by reflected as opposed to transmitted light

3. Which substances? Transition metal ions
A metal which forms one or more stable ions which have incompletely filled d orbitals
Zinc with the electronic structure [Ar] 3d104s2 doesn't count as a transition metal whichever definition you use. In the metal, it has a full 3d level. When it forms an ion, the 4s electrons are lost - again leaving a completely full 3d level.
This shortened version of the Periodic Table shows the first row of the d block, where the 3d orbitals are being filled.

4. The Origin Of Colour
Complex ions containing transition metals are usually coloured, whereas the similar ions from non-transition metals aren't. That suggests that the partly filled d orbitals must be involved in generating the colour in some way.
[Cr(H2O)6]3+
[Fe(H2O)6]2+
[Co(H2O)6]2+
[Ni(H2O)6]2+
[Cu(H2O)6]2+

5. Complex Ions These have ligands arranged around the central metal ion.
When the ligands bond with the transition metal ion, there is repulsion between the electrons in the ligands and the electrons in the d orbitals of the metal ion.
That raises the energy of the d orbitals.
However, it doesn't arrange all their energies the same amount. Instead it splits them into two groups.

6. Complex Ions
Octahedral complexes - 6 ligands around the transition metal ion, the d orbitals are always split with 2 with a higher energy than the other 3.
Tetrahedral complexes - 4 ligands around the central metal ion, when split 3 have a greater energy, and the other 2 a lesser energy.
There is an energy gap between the split groups, the size of the gap varies on with the nature of the transtion metal, it's oxidation state, and the nature of the ligands.

7. Light
When white light is passed through a soluion, some of the energy in the light is used to promote an electron from the lower set of orbitals into a space in the upper set.
Each wavelength of light has a particular energy associated with. Red light has the lowest energy in the visible region, violet light has the greatest energy.
The colour that is just right to promote is absorbed, the colour of the solution is the complementary colour
Increasing Energy
Energy of particular colour is enough to promote the electron

8. Factors Affecting the Colour of a Transition Metal Complex Ion
Nature of the Ligand – Some Ligands have strong electrical fields, causing a large energy gap, when the d orbitals split into 2 groups. Others have weaker fields producing much smaller gaps.
The size of this gap determines the wavelength of light which is absorbed., so as the splitting increases the light absorbed will shift away from the red end of the spectrum towards orange, yellow and so on.
The diagrams show some approximate colours of some ions based on chromium(III).
[Cr(OH)6]3-
[Cr(H2O)6]3+
[Cr(NH3)6]3+

9. Factors Affecting the Colour of a Transition Metal Complex Ion
The oxidation state of the metal – As the oxidation state of the metal increases, so also does the amount of splitting of the d orbitals.
Changes of oxidation state therefore change the colour of the light absorbed, and so the colour of the light you see.
The co-ordination of the ion – Splitting is different depending on the complex ions, how many ligands, if there are 6 ligands the splitting is greater than with 4 ligands.
The ion will only change co-ordination if you change the ligand – chainging the ligand will change the colour as well.
The difference in the colours is going to be a combination of the change of ligand, and the change of the number of ligands.

10. Why is copper (II) sulphate solution blue?
If white light (ordinary sunlight, for example) passes through copper (II) sulphate solution, some wavelengths in the light are absorbed by the solution.
Copper (II) ions in solution absorb light in the red region of the spectrum. The light which passes through the solution and out the other side will have all the colours in it except for the red. We see this mixture of wavelengths as pale blue (cyan).
Copper (II) sulphate solution is pale blue (cyan) because it absorbs light in the red region of the spectrum. Cyan is the complementary colour of red.