Question

Find the speed of light of wavelength lambda=600nm (in air) in a medium of refractive index 5//3 and also wavelength of this light in medium.

Answer 1

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The frequency is 5\times10^{14}\ Hz, the speed of light in the medium is 2\times10^8\ m/s and the wavelength is 4\times10^{-7}\ m.

Explanation:

Given that,

Wavelength \lambda=600 nm

Refractive index n = 1.5

We know that,

The frequency is the ratio of the speed of light and wavelength of the light.

f = \dfrac{c}{\lambda}

f = \dfrac{3\times10^8}{600\times10^{-9}}

f = 5\times10^{14}\ Hz

The speed in the medium is the ratio of the speed of the light in the vacuum and the refractive index.

n = \dfrac{c}{v}

1.5 = \dfrac{3\times10^8}{v}

v = 2\times10^8\ m/s

The wave length is the ratio of the speed of the light in the medium and frequency.

\lambda = \dfrac{v}{f}

\lambda = \dfrac{2\times10^8}{5\times10^{14}}

\lambda = 4\times10^{-7}\ m

Hence, The frequency is 5\times10^{14}\ Hz, the speed of light in the medium is 2\times10^8\ m/s and the wavelength is 4\times10^{-7}\ m.

Answer 2

Answer:

The frequency is 5\times10^{14}\ Hz, the speed of light in the medium is 2\times10^8\ m/s and the wavelength is 4\times10^{-7}\ m.

Explanation:

Given that,

Wavelength \lambda=600 nm

Refractive index n = 1.5

We know that,

The frequency is the ratio of the speed of light and wavelength of the light.

f = \dfrac{c}{\lambda}

f = \dfrac{3\times10^8}{600\times10^{-9}}

f = 5\times10^{14}\ Hz

The speed in the medium is the ratio of the speed of the light in the vacuum and the refractive index.

n = \dfrac{c}{v}

1.5 = \dfrac{3\times10^8}{v}

v = 2\times10^8\ m/s

The wave length is the ratio of the speed of the light in the medium and frequency.

\lambda = \dfrac{v}{f}

\lambda = \dfrac{2\times10^8}{5\times10^{14}}

\lambda = 4\times10^{-7}\ m

Hence, The frequency is 5\times10^{14}\ Hz, the speed of light in the medium is 2\times10^8\ m/s and the wavelength is 4\times10^{-7}\ m.

Explanation:

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