Respuesta :
Answer:
The speed of this light and wavelength in a liquid are [tex]2.04\times10^{8}\ m/s[/tex] and 442 nm.
Explanation:
Given that,
Wavelength = 650 nm
Index refraction = 1.47
(a). We need to calculate the speed
Using formula of speed
[tex]n = \dfrac{c}{v}[/tex]
Where, n = refraction index
c = speed of light in vacuum
v = speed of light in medium
Put the value into the formula
[tex]1.47=\dfrac{3\times10^{8}}{v}[/tex]
[tex]v=\dfrac{3\times10^{8}}{1.47}[/tex]
[tex]v= 2.04\times10^{8}\ m/s[/tex]
(b). We need to calculate the wavelength
Using formula of wavelength
[tex]n=\dfrac{\lambda_{0}}{\lambda}[/tex]
[tex]\lambda=\dfrac{\lambda_{0}}{n}[/tex]
Where, [tex]\lambda_{0}[/tex] = wavelength in vacuum
[tex]\lambda[/tex] = wavelength in medium
Put the value into the formula
[tex]\lambda=\dfrac{650\times10^{-9}}{1.47}[/tex]
[tex]\lambda=442\times10^{-9}\ m[/tex]
Hence, The speed of this light and wavelength in a liquid are [tex]2.04\times10^{8}\ m/s[/tex] and 442 nm.
a) The speed of this light in a liquid are 2.041 x 10⁸ m/s.
b) The wavelength of these waves in the liquid is 442 nm.
What is refractive index?
The refractive index or index of refraction is the ratio of speed of light in vacuum and speed of light in medium.
(a) speed in medium v = c/n
Where, n = 1.47 is the refraction index, c = 3 x 10⁸ m/s is the speed of light in vacuum
Then speed of the given light is
v = 3 x 10⁸ /1.47 = 2.041 x 10⁸ m/s
(b) λ/λ₀= refractive index
λ = wavelength in medium and λ₀ = wavelength in vacuum = 650 x 10⁻⁹ m
Put the value into the formula, we get
λ = 650 x 10⁻⁹/ 1.47
λ = 442 x 10⁻⁹m
Hence, The speed of this light and wavelength in a liquid are 2.041 x 10⁸ m/s and 442 nm.
Learn more about refractive index
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