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4 January, 21:14

The index of refraction for a certain type of glass is 1.645 for blue light and 1.609 for red light. A beam of white light (one that contains all colors) enters a plate of glass from the air, nair≈1, at an incidence angle of 38.55∘. What is the absolute value of?, the angle in the glass between blue and red parts of the refracted beams?

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  1. 4 January, 23:54
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    blue θ₂ = 22.26º

    red θ₂ = 22.79º

    Explanation:

    When a light beam passes from one material medium to another, it undergoes a deviation from the path, described by the law of refraction

    n₁ sin θ₁ = n₂ sin θ₂

    where n₁ and n₂ are the incident and transmitted media refractive indices and θ are the angles in the media

    let's apply this equation to each wavelength

    λ = blue

    in this case n₁ = 1, n₂ = 1,645

    sin θ₂ = n₁ / n₂ sin₂ θ₁

    let's calculate

    sin θ₂ = 1 / 1,645 sint 38.55

    sin θ₂ = 0.37884

    θ₂ = sin⁻¹ 0.37884

    θ₂ = 22.26º

    λ = red

    n₂ = 1,609

    sin θ₂ = 1 / 1,609 sin 38.55

    sin θ₂ = 0.3873

    θ₂ = sim⁻¹ 0.3873

    θ₂ = 22.79º

    the refracted rays are between these two angles
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