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19 August, 14:26

A narrow beam of light containing orange (610 nm) and blue (470 nm) wavelengths goes from polystyrene to air, striking the surface at a 28.5° incident angle. What is the angle (in degrees) between the colors when they emerge?

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  1. 19 August, 18:08
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    Answer: The angle between the two colours when they emerge is 0.4°

    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°
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