Explain to your friend, who is skeptical about energy quantization, the simple evidence provided by distinct colors you see when you hold a CD (serving as grating) near a fluorescent light. It may be helpful to contrast this evidence with the spectrum produced by an incandescent light, which relies on heating to produce a rather nonspecific blackbody spectrum.

If E is discrete, wavelength is discrete.

The wavelength of an electromagnetic radiation is related to its energy by relation:

$\mathit{E}\mathbf{=}\frac{\mathbf{h}\mathbf{c}}{\mathbf{\lambda }}$

Where, his the Planck's constant, cis the speed of light,$\lambda$is the wavelength and Eis the energy.

A CD has tiny grooves on it. Based on the size of the grooves, certain wavelengths of the light are diffracted by the CD in different directions. A fluorescent light source emits only certain wavelengths. So, when we look at a CD, illuminated by a fluorescent light source, we see only the wavelength that is diffracted at an angle towards our eye. If the wavelengths were not discrete, we would see multiple wavelengths at a time from the same spot on the CD resulting in white color.

You don't see colors when you illuminate the CD by an incandescent light source. This is because, the wavelengths emitted by an incandescent light source are not discrete, they are continuous and their intensity depends on the temperature of the heating filament. Continuous means all wavelengths are present. You cannot say that this particular wavelength is absent in this incandescent light source.