(f=5.09×1014hz) has a wavelength of 589 nanometers in air. what is the wavelength of this light in lucite? (1) 150 nm (3) 589 nm (2) 393 nm (4) 884 nm

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.