What is metamerism?

Hint: Metamerism is a type of structural isomerism. Metamers have the same functional group and same molecular formula. But metamers have different structural formulas.

Complete answer:
Isomerism is the phenomenon in which two or more compounds have the same molecular formula but different structural formula. The compounds showing this phenomenon are known as isomers of each other. You can broadly classify isomerism into two types, structural isomerism (or constitutional isomerism) and stereoisomerism. You can classify structural isomerism into chain isomerism, position isomerism, functional group isomerism, metamerism, tautomerism and ring chain isomerism. You can classify stereoisomerism into geometrical isomerism and optical isomerism.
Metamers are the isomers having the same molecular formula but different alkyl groups on two sides of functional groups. This phenomenon of isomerism is called metamerism.
You can give an example of diethyl ether and methyl propyl ether. The structural formula of diethyl ether and methyl propyl ether are \[{\text{C}}{{\text{H}}_{\text{3}}}{\text{C}}{{\text{H}}_{\text{2}}}{\text{OC}}{{\text{H}}_{\text{2}}}{\text{C}}{{\text{H}}_{\text{3}}}\] and \[{\text{C}}{{\text{H}}_{\text{3}}}{\text{OC}}{{\text{H}}_{\text{2}}}{\text{C}}{{\text{H}}_{\text{2}}}{\text{C}}{{\text{H}}_{\text{3}}}\] respectively. Both have the same molecular formula of \[{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}{\text{O}}\] .
Both diethyl ether and methyl propyl ether have ether functional groups. The general formula of ethers is \[{\text{R}} - {\text{O}} - {\text{R}}\] .
For diethyl ether, two R groups are two ethyl groups. For methyl propyl ether, one R group is methyl group and another R group is propyl group. Methyl, ethyl and propyl groups can be represented as \[{\text{C}}{{\text{H}}_{\text{3}}}{\text{, C}}{{\text{H}}_{\text{3}}}{\text{C}}{{\text{H}}_{\text{2}}},{\text{ C}}{{\text{H}}_{\text{3}}}{\text{C}}{{\text{H}}_{\text{2}}}{\text{C}}{{\text{H}}_{\text{2}}}\] respectively.
Usually molecules having divalent oxygen atom or Sulphur atom shows metamerism. In these molecules, the divalent oxygen or Sulphur atom is surrounded by alkyl groups.

Note: You can consider primary, secondary and tertiary amines as metamers provided they have the same molecular formula. Thus, n propyl amine, ethyl methyl amine and trimethyl amine all are metamers. They have same molecular formula of \[{{\text{C}}_{\text{3}}}{{\text{H}}_{\text{9}}}{\text{N}}\]. The structural formulae of primary, secondary and tertiary amines are \[{\text{C}}{{\text{H}}_{\text{3}}}{\text{C}}{{\text{H}}_{\text{2}}}{\text{C}}{{\text{H}}_{\text{2}}}{\text{N}}{{\text{H}}_{\text{2}}}{\text{, C}}{{\text{H}}_{\text{3}}}{\text{C}}{{\text{H}}_{\text{2}}}{\text{NHC}}{{\text{H}}_{\text{3}}}{\text{ and }}{\left( {{\text{C}}{{\text{H}}_{\text{3}}}} \right)_3}{\text{N}}{{\text{H}}_{\text{2}}}\] respectively.