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The wavelength of light changes as light goes from one medium to another, while the frequency remains the same. Is the wavelength longer or shorter in water than in air? Explain in terms of the equation speed 5 frequency 3 wavelength.
A certain orange light has a wavelength of 600 nm (6 3 1027 m) in air. What is its wavelength in water, where light travels at 75% of its speed in air? In Plexiglas, where light travels at 67% of its speed in air?

Respuesta :

Answer:

λw = 450 nm

λg = 402 nm

Explanation:

Frequency of a wave is defined as the number of vibrations coming out of the source in one second.

The frequency of a wave is the fundamental property of the source.

The relation among the wavelength, wave velocity and frequency is given by

wave velocity = frequency x wavelength

Frequency is constant while the velocity and wavelength changes.

wavelength in air, λa = 600 nm

Let the wavelength in water is λw.

speed of light in air, c = 3 x 10^8 m/s

speed of light in water = 75 % of c = 0.75 x 3 x 10^8 = 2.25 x 10^8 m/s

speed of light in plexglass = 67 % of c = 0.67 x 3 x 10^8 = 2.01 x 10^8 m/s

[tex]\frac{\lambda _{w}}{\lambda _{a}}=\frac{velocity in water}{velocity in light }[/tex]

[tex]\lambda _{w}=600\times \frac{2.25\times 10^{8}}{3\times 10^{8}}[/tex]

λw = 450 nm

[tex]\frac{\lambda _{g}}{\lambda _{a}}=\frac{velocity in glass}{velocity in light }[/tex]

[tex]\lambda _{g}=600\times \frac{2.01\times 10^{8}}{3\times 10^{8}}[/tex]

λg = 402 nm