Wavelength of light changing from air to water at 0.700c

[Kickbladesama]

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

 

[G01]

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:

$$\lambda f=v$$

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

$$v=c/n$$, where n is the index of refraction of the medium.

c is the speed of light in a vacuum:

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

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

Using this information, can you solve the problem?

 

[Kickbladesama]

thanks for help

 

[Kickbladesama]

how do i do this problem?

 

[Redbelly98]

As GO1 said, use the relation between wavelength, frequency, and speed:

f = v/λ

And this:

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.