A beam of light has a wavelength of 620 nm in vacuum. a. What is the speed of this light in a liquid whose index of refraction at this

Question

A beam of light has a wavelength of 620 nm in vacuum.
a. What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.56? (Use 3.00×108 m/s for the speed of light in a vacuum.)
b. What is the wavelength of these waves in the liquid?

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Thông Đạt 6 months 2021-07-30T08:10:19+00:00 1 Answers 12 views 0

Answers ( )

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    2021-07-30T08:11:56+00:00

    Explanation:

    It is given that,

    Wavelength of a beam of light in vacuum, \lambda_o=620\ nm

    (a) Let v is the speed of light in a liquid whose index of refraction at this wavelength is 1.56.

    We know that,

    Refractive index,

    n=\dfrac{c}{v}\\\\v=\dfrac{c}{n}\\\\v=\dfrac{3\times 10^8}{1.56}\\\\v=1.92\times 10^8\ m/s

    (b) The wavelength of light in material,

    \lambda=\dfrac{\lambda_o}{n}

    Let \lambda_1 is the wavelength of these waves in the liquid. So,

    \lambda_1=\dfrac{\lambda_o}{n}\\\\\lambda_1=\dfrac{620\times 10^{-9}}{1.56}\\\\\lambda_1=3.97\times 10^{-7}\ m

    Hence, this is the required solution.

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