Answer: The angle between the two colours when they emerge is 0.4°
Step-by-step explanation:
The refracting angle for different colors knowing its refractive index can be calculated using Snell's law.
Ni × sin α = Nr × sinβ
Where Ni is the refractive index for light in incident medium
α is the angle the incident makes with normal
Nr is the refractive index for light in the refractive medium
β is the angle the refracted makes with the normal
Making β the subject
β = arcSin ( Ni × sinα)/Nr
For Orange color
The value of refractive index in polystyrene medium is 1.490 ,that is Ni= 1.490
α is 30° and Nr is the refractive index of air = 1
β = arcSin(1.490×sin30°)/1
β= 48.15°
For Blue color
The value of refractive index in polystyrene medium is 1.499,that is Ni= 1.499
α is 30° and Nr is the refractive index of air = 1
β = arcSin(1.499×sin30°)/1
β= 48.55°
The angle between the two colours is the difference in the angles of their refracted rays
48.55-48.15=0.4°