Final answer:
To find the angle between the yellow (580 nm) and green (550 nm) colors when they emerge from polystyrene to air, Snell's Law must be used, involving each color's specific refractive index in polystyrene. The difference in their angles of refraction when entering the air reveals the angle between the colors.
Step-by-step explanation:
To determine the angle between the colors as they emerge from polystyrene to air, we need to use Snell's Law, which relates the angle of incidence to the angle of refraction via the indices of refraction for the two media. This law is stated as: n1 * sin(θ20) = n2 * sin(θ21), where n1 and n2 are the indices of refraction for the first and second medium respectively, θ20 is the angle of incidence, and θ21 is the angle of refraction.
First, we will find the refractive index of polystyrene for both yellow (580 nm) and green (550 nm) wavelengths using established refractive indices or a provided table. After finding the refractive indices, we apply Snell's Law for each color to find its angle of refraction when passing into air.
The incident angle is given as 30.0°, and the refractive index of air can be approximated as 1. The refractive index for polystyrene must be provided or known for precise wavelengths. Once we find the refractive angles for both colors, we can calculate the difference between them, which is the answer we're looking for.
Note that without the refractive indices for the specific wavelengths in polystyrene, we cannot calculate the actual angle difference, so it is assumed that this information is available to calculate the answer.