Step 1: Understanding S–O–S linkage.
An S–O–S linkage refers to a structure in which two sulphur atoms are connected through an oxygen atom. Such linkages are found in certain condensed oxyacids of sulphur.
Step 2: Analyze each option.
(A) $H_2S_2O_4$: This compound does not contain an S–O–S bridge; the sulphur atoms are not linked through oxygen.
(B) $H_2S_2O_5$: This is pyrosulphurous acid, which contains an S–O–S linkage between the two sulphur atoms.
(C) $H_2S_2O_3$: Thiosulphuric acid contains an S–S bond, not an S–O–S linkage.
(D) $H_2S_2O_2$: This compound does not show an S–O–S linkage.
Step 3: Conclusion.
Among the given options, only $H_2S_2O_5$ contains an S–O–S linkage.