Question

Light rays that enter your eye are affected by the fluid that fills the eyeball, called the vitreous humor (Figure 1). When red light from a λ=633nm helium–neon laser enters your eye, its wavelength drops to 474 nm. Use this information to calculate the index of refraction of the vitreous humor and the speed and frequency of light passing through it.

A) The newest laser pointers emit light with a wavelength of λ0=555nm in air. What is the wavelength of this light in the vitreous humor of the eyeball?

Answer 1

In the phenomenon of refraction, frequency remains constant.

Since speed of light is decreased when light passing from optically rarer medium

to optically denser medium and frequency remains constant, wavelength decreases.

frequency of given red light = c / ( 633 $\times$ 10^-9 ) Hz

where c is speed of light in air

If wavelength drops to 474 nm, then speed of light v in vitreous humor is given by,

v = [ c / ( 633 $\times$ 10^-9 ) ] $\times$ ( 474 $\times$ 10^-9 ) = 0.749 c

refractive index $\mu$ = speed of light in air / speed of light in medium = c / ( 0.749 c )

refractive index $\mu$ = 1.335

speed of light = 0.749 $\times$ 3 $\times$ 10⁸ m/s = 2.246 $\times$ 10⁸ m/s

-----------------------------------------------------------------------------

new wavelength in air $\lambda$ _a = 555 nm

if wavelength in vitreous humor is $\lambda$ _v , then we have , [ c/(555 $\times$ 10^-9 ) ] $\times$ $\lambda$_v = 0.749 c

hence $\lambda$ _v = 0.749 $\times$ 555 $\times$ 10^-9 = 416 $\times$ 10^-9 m = 416 nm