The indices of refraction for violet light (λ = 400 nm) and red light (λ = 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of ligh

Question

The indices of refraction for violet light (λ = 400 nm) and red light (λ = 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 51.0 ∘ to the normal.

Calculate the angular separation between these two colors of light in the refracted ray.

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Thu Nguyệt 4 years 2021-07-26T17:06:22+00:00 1 Answers 291 views 0

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  1. thuthuy
    0
    2021-07-26T17:07:39+00:00
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    Answer:

    0.42°

    Explanation:

    Using Snell’s law of refraction which states that the ratio of the angle of sin of incidence to angle of sine of refraction is equal to a constant for a given pair of media. Mathematically,

    Sin(i)/sin(r) = n

    n is the refractive index of the medium

    FOR VIOLET LIGHT:

    n = 2.46

    i = 51°

    r = ?

    To get r, we will use the Snell’s law formula.

    2.46 = sin51°/sinr

    Sinr = sin51°/2.46

    Sinr = 0.316

    r = sin^-1(0.316)

    rv = 18.42°

    FOR RED LIGHT:

    n = 2.41

    i = 51°

    r = ?

    To get r, we will use the Snell’s law formula.

    2.41 = sin51°/sinr

    Sinr = sin51°/2.41

    Sinr = 0.323

    r = sin^-1(0.323)

    rd = 18.84°

    The angular separation between these two colors of light in the refracted ray will be the difference between there angle of refraction.

    Angular separation = rd – rv

    = 18.84° – 18.42°

    = 0.42°

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