A certain kind of glass has an index of refraction of 1.660 for blue light of wavelength 420 nm and an index of 1.630 for red light of wavel

Question

A certain kind of glass has an index of refraction of 1.660 for blue light of wavelength 420 nm and an index of 1.630 for red light of wavelength 690 nm. If a beam containing these two colors is incident at an angle of 30.0° on a piece of this glass, what is the angle between the two beams inside the glass?

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MichaelMet 4 years 2021-07-29T20:22:04+00:00 1 Answers 31 views 0

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  1. Doris
    0
    2021-07-29T20:23:18+00:00
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    Answer:

    Explanation:

    Using Snell’s law

    n₁ sinθ₁ = n₂ sinθ₂

    for 420 nm wavelength

    where n₁ = 1.00 ( refractive index of air) and θ₁ = 30° n₂ = 1.660

    1.00 × sin 30° = 1.660 sinθ₂

    sinθ₂ = 0.3012

    θ₂ = sin⁻¹ 0.3012 = 17.53°

    for 690 nm wavelength

    n₁ sinθ₁ = n₂ sinθ₂

    sinθ₂ = 0.5 / 1.630

    θ₂ = sin⁻¹ 0.3067 = 17.86°

    the angle between the two beam = 17.863° – 17.53° = 0.333°

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