The fluorescent light does not come out immediately - the luminous watch will be visible for a long time after the stimulus. In the case of the fluorescent lamp the emission is more prompt, with a shorter life, so that flickering at 100 or 120 Hertz is occasionally seen.

The fading of the luminosity goes according to an exponential, a function that is very common in nature.  It is found in radioactivity, and in any other process where the rate of change of a variable is proportional to the variable itself.  Sometimes a fluorescent substance has more than one time-constant.  Each generates an exponential, but the overall curve is complicated, until only the longest-lived component is left.  Some radar tubes have had phosphors with two different decay times.

You can see fluorescence using a flash-gun to excite the cathode ray tube in a TV or a computer.  In a dark room, place your hand on the screen with your fingers spread.  Shut your eyes.  With the flash gun set to manual, if possible, to get maximal intensity, press the button, remove your hand from the screen, and open your eyes.  You will see a fading silhouette of your hand.  A torch will do if held very close, but it makes a much feebler effect.  A luminous clock or watch can of course be excited in the same way.  The green screen of an oscilloscope works even better than a television set.

Usually the wavelength of the emitted light is longer than the wavelength of the incident light.  The relevant fact is that the frequency of the outgoing light is lower than that of th incoming light.  Light behaves as if it is emitted and absorbed in small particles, called photons.  The energy of a photon is proportional to the frequency of the light.  So in fluorescence, the emitted photons are less energetic than the incident ones.

Some phenomena are related to frequency and some to wavelength.

Atoms can actually be stimulated to emit by photons of exactly the same energy as the ones they emit.  The new photons are exactly in step with the original ones.  This is the basis of lasers.   A laser provides a lot of atoms in a state in which they are ready to emit, and a means of making sure that they are hit by some light.  The resulting beam consists of a wave of light with all the photons in step.  Lasers

Some old clocks and watches used radioactive materials to produce light.  The particles from the decay of radioactive nuclei provided energy to stimulate the atoms or molecules in the paint.  Zinc sulphide glows well when energized in this way.

Some substances can be stimulated to emit light by bombardment with electrons.  The pictures below show the screen of a measuring instrument which has a cathode ray tube like the ones in television receivers and desk-top computers.

Three beams of electrons are swept over the screen.  The beams land on three different types of material, called phosphors, which glow red, green and blue respectively when given energy by the beams.  TFT screens work in a different way, but they also convert electrical energy into light energy.

As with fluorescence, the light does not come out immediately.  In a TV, the response must be quick, or moving images will be smeared.  But in a radar screen, where the electron beam scans in synchronism with the rotating antenna, the persistence of the light needs to be quite long, to keep the picture filled in between visits from the beam - 

The picture below shows light from an 11 W fluorescent lamp, coming off a compact disc.  Although the light was not sent through a narrow slit, which would have improved the image, you can see that the spectrum is clearly not continuous.

 Fluorescent light is very unsuitable for colour matching.  Although it can be made to look almost white to the eye, this is not enough.  The process of evaluating colour is affected by the spectrum of the incident light, the spectrum of the reflecting object, the spectral responses of the three types of colour receptors in the eye, and the interpretational powers of the eye-brain combination.  

For example, yellow light might be formed by a narrow spectral spread, as in the sodium lamp used for street lighting, or it might be formed by a wide spectrum of red, orange and green.  Similarly, a yellow object might reflect in only a narrow yellow band of light, or it might reflect green and red, but not yellow.  These two objects would respond in totally different ways to the two light sources.

The pictures below show the same objects illuminated by daylight, electronic flash gun, incandescent filament lamp, and tubular fluorescent lamp.  Daylight slide film was used.