To find the wavelength of the monochromatic light in Lucite, we need the index of refraction of Lucite which is n=1.5 and the formula λ₀/λ=n, where λ₀ is the wavelength in the air, λ is the wavelength in Lucite and n is the index of refraction of Lucite.
In our case λ₀=589 nm=589*10^-9 m.
We need to solve λ₀/λ=n for λ:
λ=λ₀/n=(589*10^-9)/1.5= 392.67*10^-9 which is very close to
393*10^-9 m = 393 nm.
So the wavelength of the monochromatic light in Lucite is: λ=393 nm.
