The wavelength of a helium-neon laser beam in air is 633nm, and it takes 1.38 ns for the beam to travel through 30cm of an unknown liquid. To find the wavelength in the liquid, the index of refraction can be calculated using the formula n=c/v, where c is the speed of light and v is the speed of light in the liquid. The time and distance provided allow for the calculation of the speed of light in the liquid. Once the index of refraction is determined, the wavelength in the liquid can be found by dividing the wavelength in air by the index of refraction. This approach provides a clear path to solving the problem without needing additional information.