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22 January, 16:23

The frequency of a light wave in air is 4.6 * 10¹⁴ Hz. What is the wavelength of this wave after it enters a pool of water?

300 nm

490 nm

650 nm

870 nm

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Answers (1)
  1. 22 January, 18:12
    0
    490 nm

    Explanation:

    Wave length: This is the distance of a complete cycle covered by a wave.

    The expression for frequency, wave length and speed is given as,

    c = λf ... Equation 1

    Where c = speed of light in water, λ = wave length of light, f = frequency of light.

    Also,

    n = v/c ... Equation 2

    Where n = refractive index of water, v = speed of sound in air.

    Making c the subject of the equation,

    c = v/n ... Equation 3

    Substitute equation 3 into equation 2

    v/n = λf

    make λ the subject of the equation

    λ = v/nf ... Equation 4

    Given: f = 4.6 * 10¹⁴ Hz

    Constant: n = 1.33, v = 3.0*10⁸ m/s.

    Substitute into equation 4

    λ = 3.0*10⁸ / (1.33*4.6 * 10¹⁴)

    λ = 0.49*10⁻⁶ m

    λ = 490 nm.

    Hence the right option is 490 nm
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