Answer:
The color blue emerges at 19.16° and the color red emerges at 19.32°.
Explanation:
The angle at which the two colors emerge can be calculated using the Snell's Law:
[tex]n_{1}sin(\theta_{1}) = n_{2}sin(\theta_{2})[/tex]
Where:
n₁ is the refractive index of the incident medium (air) = 1.0003
n₂ is the refractive index of the refractive medium:
blue light in crown glass = 1.524
red light in crown glass = 1.512
θ₁ is the angle of the incident light = 30°
θ₂ is the angle of the refracted light
For the red wavelengths we have:
[tex] \theta_{2} = arcsin(\frac{n_{1}sin(\theta_{1})}{n_{2}}) = arcsin(\frac{1.0003*sin(30)}{1.512}) = 19.32 ^{\circ} [/tex]
For the blue wavelengths we have:
[tex] \theta_{2} = arcsin(\frac{n_{1}sin(\theta_{1})}{n_{2}}) = arcsin(\frac{1.0003*sin(30)}{1.524}) = 19.16 ^{\circ} [/tex]
Therefore, the color blue emerges at 19.16° and the color red emerges at 19.32°.
I hope it helps you!
