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2 April, 03:07

A laser beam is incident at an angle of 29.4° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.84° 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 (c) Find its frequency in the solution (d) Find its speed in the solution

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  1. 2 April, 03:19
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    a) For the ray going into syrup, angle of incidence (i) is 29.4 and angle of refraction (r) is 18.84

    Refractive index of syrup = Sin i / Sin r

    = Sin 29.4 / Sin 18.84

    = 1.51.

    b) The wavelength of a light is reduced in a medium by the factor of refractive index so

    wavelength in the medium

    = Wavelength in air / refractive index of the solution

    = 632.8 / 1.51

    = 419.07 nm.

    The frequency remains unchanged. The frequency in the medium will be same as that in air or vacuum.

    Frequency in air = Velocity of light in air / wavelength in light

    = 3 x 10⁸ / 632.8 x 10⁻⁹

    = 4.74 x 10¹⁴ Hz.

    Frequency in the medium is same as that in air.

    Velocity in the medium

    V = velocity in air / refractive index

    = 3 x 10⁸ / 1.51

    = 1.98 x 10⁸ m / s
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