Question

The intensity of reflection of various wavelengths of light projected onto the eye can be used to determine the thickness of the tear film that coats the cornea. The tear film and cornea have indices of refraction 1.331 and 1.373, respectively. When white light is incident on the cornea, strong reflected intensities appear at wavelengths (in air) of 480 nm and 520 nm, but no wavelengths between them. What is the thickness of the tear film?

Answer 1

n_t = index of refraction of tear film = 1.331

t = thickness of the film = ?

= wavelength

for strong reflection , we have

2 n_t t = m

for ₁ = 480 nm

2 n_t t = m₁₁                                                      eq-1

and

for ₂ = 520 nm

2 n_t t = m₂₂                      eq-2

Using eq-1 and eq-2

m₂₂ = m₁₁  

m₂ (520) = m₁ (480)

m₁ /m₂ = 13/12

comparing , we get

m₂ = 12

using eq-2

2 n_t t = m₂₂  

2 (1.331) t = (12) (520)

t = 2344.1 nm

t = 2.34 x 10^-6 m