A laser beam is incident at an angle of 29.8° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.62°

Question

A laser beam is incident at an angle of 29.8° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.62° to the vertical, what is the index of refraction of the syrup solution? (b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution.

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Neala 5 years 2021-07-31T22:16:05+00:00 1 Answers 32 views 0

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  1. taiduc
    0
    2021-07-31T22:17:58+00:00
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    Answer:

    (a) 1.5

    (b) 421.86 * 10^{-9} m

    Explanation:

    Angle of incidence, i = 29.8°

    Angle of refraction, r = 18.62°

    (a) Index of refraction is given as:

    n = \frac{sin(i)}{sin(r)}

    n = \frac{sin(29.8)}{sin(18.62)} \\\\\\n = \frac{0.4970}{0.3193} \\\\\\n = 1.5

    The refractive index of the syrup is 1.5.

    (b) Wavelength of the red light in a vacuum, λ(1)  = 632.8 nm = 632.8 * 10^{-9} m

    Refractive index is also a ratio of the speed of the light in a vacuum with the speed of light in a particular medium:

    n = \frac{c}{v}

    The speed of light in a vacuum is given as;

    c = λ(1) * f

    => f = c/λ(1)

    The speed of light in a medium is given as;

    v = λ(2) * f

    => f = v/λ(2)

    (λ = wavelength and f = frequency)

    We know that the frequency of light does not change when it changes media, hence, we can equate both frequencies:

    c/λ(1) = v/λ(2)

    Therefore:

    c / v = λ(1) / λ(2)

    Therefore, refractive index will become:

    n = λ(1) / λ(2)

    => 1.5 =  632.8 * 10^{-9} / λ(2)

    The wavelength of the red light in the solution is therefore:

    λ(2) = 632.8 * 10^{-9} / 1.5

    λ(2) = 421.86 * 10^{-9} m

    The wavelength of the light in the solution is 421.86 * 10^{-9} m

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