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4 June, 20:46

A laser beam with vacuum wavelength 20 = 632.8 nm is incident at an angle of 30.0° from the vertical (in air) into a solution of corn syrup. If the beam is refracted to 19.24° from the vertical, find the following quantities: (Sketch the question; include a normal line.) a) Index of refraction of the solution b) Frequency of light in the solution c) Speed of light in the solution d) Wavelength of light in the solution

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  1. 5 June, 00:32
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    (a) 1.517

    (b) 4.74 x 10^14 Hz

    (c) 1.98 x 10^8 m/s

    (d) 417.14 nm

    Explanation:

    wavelength in air, λa = 632.8 nm

    Angle of incidence, i = 30 degree

    angle of refraction, r = 19.24 degree

    (a) According to the Snell's law

    refractive index, μ = Sin i / sin r = Sin 30 / Sin 19.24 = 0.5 / 0.3295 = 1.517

    (b) Frequency always remains constant in case of refraction or reflection.

    Velocity of light in air = frequency x wavelength in air

    Frequency = (3 x 10^8) / (632.8 x 10^-9) = 4.74 x 10^14 Hz

    (c) let the speed of light in solution is v.

    refractive index of solution = speed of light in air / speed of light in solution

    1.517 = 3 x 10^8 / v

    v = 3 x 10^8 / 1.517 = 1.98 x 10^8 m/s

    (d) Let the wavelength of light in solution is λs.

    refractive index of solution = wavelength in air / wavelength in solution

    λs = 632.8 / 1.517 = 417.14 nm
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