Short Answer 
The refracted wavelength of light when transitioning from one medium to another with a different refractive index can be calculated using the equation n‚CA¬∑Œª‚CA = n‚CC¬∑Œª‚CC. Given a refractive index of 1 for air and Œª‚CA of 600 nm, with n‚CC as 4/3, the refracted wavelength Œª‚CC is computed to be 450 nm.
Step 1: Understand Refraction and Wavelength Change
When light travels from one medium to another that has a different refractive index, it undergoes a change in wavelength while maintaining a constant frequency. The relationship between the refractive indices and wavelengths of the two media is described by the equation:
- n1·≈í¬™1 = n2·≈í¬™2
Step 2: Identify Given Values
To determine the refracted wavelength, identify the known values in the equation: n1 is the refractive index of the first medium (commonly air, taken as 1), and λ1 is the incident wavelength (600 nm). For the second medium, given that n2 is 4/3, you can compute the values needed for the equation.
Step 3: Apply the Formula to Calculate the Wavelength
Substituting the given values into the formula yields:
- 1(600) = (4/3)·≈í¬™2
- Rearranging gives ≈í¬™2 = 600·(3/4)
- Finally, calculate λ2 = 450 nm
This value represents the wavelength of the light after it has been refracted through the second medium.