We discuss, in terms of particle acceleration, the results from optical VLT observations of hot spots associated with radio galaxies. On the basis of observational and theoretical grounds, the following is shown. (i) Relatively low radio-radio power hot spots are the optimum candidates for being detected at optical waves. This is supported by an unprecedented optical detection rate of 70 per cent out of a sample of low radio power hot spots. (ii) The shape of the synchrotron spectrum of hot spots is mainly determined by the strength of the magnetic field in the region. In particular, the break frequency, related to the age of the oldest electrons in the hot spots, is found to increase with decreasing synchrotron power and magnetic field strength. Both observational results are in agreement with an in-situ particle acceleration scenario.