Wavelength of Light: 0.544µm in Air & Water

The speed of light in air and water are different, so use the second equation:v = c/nWhere n is the index of refraction for the medium (air or water). Rearrange this equation to solve for v, and plug it into the first equation. Then you can solve for the wavelength in water.
  • #1
Kickbladesama
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0

Homework Statement


Light of wavelength 0.544 µm (in air) enters the water in a swimming pool. The speed of light in water is 0.700 times the speed in air. What is the wavelength of the light in water?


Homework Equations


mu = m / L

v = sqrt (F/mu)

speed of air 386 m/s

The Attempt at a Solution


0.700 x 386 = 270.2

270.2 = sqrt (F / 0.544) = 39716.40

F = 39716.40

idk what to do now
 
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  • #2
The equations you are using do not apply to light waves. Your formula for a velocity is for a mechanical wave on a string, not a light wave. 386m/s is NOT the speed of light in air, not even close.

Forgive me if I'm wrong, but it seems you are trying to plug and chug equations to get an answer for this problem without even considering what the equations mean. You have to go and seriously read the chapter on this topic in your book if you haven't done so. Trying to mindlessly plug an chug equations is a recipe for disaster in a physics course.

I will give you a few hints to get you on the right path:

The speed of light is related to the light's wavelength and frequency by:

[tex]\lambda f=v[/tex]

The speed of the light depends on the medium and is given by:

[tex]v=c/n[/tex], where n is the index of refraction of the medium.

c is the speed of light in a vacuum:

[tex]c=\lambda_{vac}f=3*10^8 m/s[/tex]

The frequency of the light will remain the same in all media.

Using this information, can you solve the problem?
 
  • #3
thanks for help
 
  • #4
how do i do this problem?
 
  • #5
As GO1 said, use the relation between wavelength, frequency, and speed:

f = v/λ

And this:

G01 said:
The frequency of the light will remain the same in all media.

Using the fact that f is the same for the light in air or water, work with the above equation.
 

FAQ: Wavelength of Light: 0.544µm in Air & Water

What is the significance of the wavelength of light being 0.544µm in both air and water?

The wavelength of light being the same in both air and water is significant because it allows for consistent measurements and calculations in both media. This is useful for scientists studying the behavior of light in different environments.

How does the wavelength of light change when it enters water from air?

The wavelength of light decreases when it enters water from air. This is due to the change in the speed of light in different media. In water, light travels at a slower speed, resulting in a shorter wavelength.

Is the wavelength of light in air and water affected by the color of the light?

Yes, the wavelength of light in air and water is affected by the color of the light. Different colors of light have different wavelengths, and this remains true in both air and water. However, the amount of change in the wavelength may vary depending on the color.

How does the wavelength of light in air and water affect the perception of color?

The wavelength of light in air and water can affect the perception of color. Water tends to absorb longer wavelengths, such as red, more easily than air. This can cause objects to appear slightly different in color when viewed underwater compared to when viewed in air.

Can the wavelength of light in air and water be calculated using a formula?

Yes, the wavelength of light in air and water can be calculated using the formula λ = c / f, where λ is the wavelength, c is the speed of light in a vacuum, and f is the frequency of the light wave. This formula applies to all media, including air and water.

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