Question

speed of light in air = 2.998*10^8 ms
speed of light in cornea = 2.181*10^8 ms
refractive index of cornea = 1.4
if the wavelength of light in air =520nm what is its wavelength in the cornea?

Answer 1

(i) before entering the interior of the eye, light has to travel through 2mm of cornea, which takes ca. 9.17 ps. calculate the refractive index of th cornea.

ans:1.4

(ii) if th light in part (ii) has a wavelength of 520nm, what is th wavelength in th cornea?

Answer 2

The relative refractive indices are the ration of the speed of light in the different materials. Thus \[\frac{n_1}{n_2}=\frac{v_2}{v_1}\]. This comes from the fact that the refractive index of a material is \[n=\frac{c}{v}\]. for two materials of index \(n_1\) and \(n_2\) we would have \[\frac{n_1}{n_2}=\frac{c}{v_1}\frac{v_2}{c}\].

But we recall that for waves \(v=f\lambda\) but that the frequency will be constnat in any refractive material. Thus, we can say that
\[\frac{n_1}{n_2}=\frac{v_2}{v_1}=\frac{\lambda_2}{\lambda_1}\]

We can now solve the question. Refractive index of air is 1, for the cornea it is 1.4 and wavelength in air is 540 nm. hence \[\frac{1.4}{1}=\frac{\lambda_{2}}{540\times10^{-9}}\]. hence \[\lambda_2=1.4\times540\times10^{-9}=756\times10^{-9}\]

so the answer is \(\lambda=756\) nm. You can try it with using the speeds of the light instead of the refractive index to get the same answer.

Answer 3

@ Fil Rouge, The wavelength does change, but its frequency remains constant in the two materials.

Answer 4

Exactly ! Sorry.... Mea Culpa !

Answer 5

thank you again! i think you may have helped me with this before but my tutor started showing me a different way of doing it and never finished which confused me!

the next question asks the frequency! :)

Answer 6

I remember helping before, but it is no problem, in physics, there are many ways to radiate a cat ;) Frequency is easy. Remember it is constant in air and in the cornea, so you can work it out from the speed of light and wavelength in respective material. I.e. \[v_{air}=f\times\lambda_{air}\] or \[v_{cornea}=f\times\lambda_{cornea}\]. If you work it out both ways you will find the answer for frequency being the same.