The backing voltage in a photomultiplier tube (PMT) depends on the frequency of the incident light but not on its intensity. This is because the backing voltage is determined by the energy of the incident photons, which is proportional to their frequency. The intensity of the light, on the other hand, is determined by the number of photons incident on the PMT per unit time, which does not affect the backing voltage.

In a PMT, the incident photons strike a photocathode, which emits electrons through the photoelectric effect. The emitted electrons are then accelerated towards a series of dynodes, each of which multiplies the number of electrons through secondary emission. The final output signal is proportional to the number of electrons that reach the anode, which in turn is proportional to the number of incident photons.

The backing voltage is applied between the photocathode and the first dynode. It serves to accelerate the emitted electrons towards the dynodes, and its value is chosen to ensure that the electrons have sufficient energy to cause secondary emission. The backing voltage is typically a few hundred volts, and it does not need to be adjusted for different light intensities.

The frequency of the incident light, on the other hand, does affect the backing voltage. This is because the energy of a photon is proportional to its frequency, so higher-frequency photons have more energy than lower-frequency photons. In order to ensure that the emitted electrons have sufficient energy to cause secondary emission, the backing voltage must be increased for higher-frequency light.

Therefore, the backing voltage in a PMT depends on the frequency of the incident light, but not on its intensity.