Spectrum of Light
> What would the spectrum of laser look like?
The spectrum of laser varies based on the type of the laser. Lasers differ to each other by the operation wavelengths. Since most lasers  have one or a few operation wavelengths, the spectrum of laser should strike at the operation wavelengths.
> Why is the refraction index dependent on wavelength?
The friction of electron in a media and the electronic field of a light (in certain wavelength(s)) changes the movement of the electron.
 List of laser types. https://en.wikipedia.org/wiki/List_of_laser_types
 Why do prisms work (why is refraction frequency dependent)? https://physics.stackexchange.com/questions/65812/why-do-prisms-work-why-is-refraction-frequency-dependent