If a beam of light from a He-Ne laser has wavelength 543 nm in air, what is its wavelength in water? The index of refraction for water is 1.33.

722 nm , 408 nm , 540 nm , or 360 nm ?

Question

If a beam of light from a He-Ne laser has wavelength 543 nm in air, what is its wavelength in water? The index of refraction for water is 1.33. 

722 nm , 408 nm , 540 nm , or 360 nm ?

michele_laino · Answer

the light speed v in water is:
$$v = \frac{c}{n}$$

michele_laino · Answer

n is the refractive index of water

anonymous · Answer

ok! what can we plug in? :/

michele_laino · Answer

we can write this:
$${\lambda _2}\nu  = \frac{{{\lambda _1}\nu }}{n}$$

michele_laino · Answer

since the frequency is the same inside those two mediums, then we have:
$$\Large {\lambda _2} = \frac{{{\lambda _1}}}{n}$$

where \lambda_1=543 nm, and \lambda_2 is the requested wavelength

anonymous · Answer

okay! so we plug in 543/n? what is n?

michele_laino · Answer

n=1.33

anonymous · Answer

so we get 408? 408 nm is our solution?

michele_laino · Answer

$$\Large   {\lambda _2} = \frac{{{\lambda _1}}}{n} = \frac{{543}}{{1.33}} = ...$$

michele_laino · Answer

yes! That's right!

anonymous · Answer

yay!! thank you:)

michele_laino · Answer

:)