Question

Why are different colours observed in octahedral and tetrahedral complexes for the same metal and same ligands?

Answer 1

The extent of the splitting of d-orbitals is different in the octahedral and tetrahedral field. CFSE in octahedral and tetra federal field are closely related as.

${△}_t=\left(\frac{4}{9}\right){△}_0$

Where the Crystal field splitting energy in tetrahedral filed
The wavelength of light and CFSE are related to each other by formula

${△}_0=E=\frac{hc}{\lambda }E\propto \frac{1}{\lambda }$

So, a higher wavelength of light is absorbed in octahedral complexes than tetrahedral complexes for same metal and ligands. Thus, different colours are observed.