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how to measure the wavelengths of ultraviolet radiation isn't it invisible? it's possible to measure visible radiation but how to measure invisible radiation?

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It's common to measure spectra in the non-visible region and UV or infra-red spectrometers are available off the shelf. Google for many, many manufacturers of the kit. Also see the Wikipedia articles on UV spectroscopy and infrared spectroscopy.

Typically UV and IR spectrometers will use a diffraction grating to disperse the light and a photomultiplier tube to detect the radiation.

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Three different ways (at least).

1) Use a detector, like a photodiode or photomultiplier, which responds to UV by producing electrons when hit by photons even if those photons are not visible,

2) Use a detector, like a bolometer, which measures the temperature rise produced when UV energy is absorbed, or

3) Coat a visible-only detector with a phosphor which emits light when hit with UV, then detect the emitted visible light.

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