Question

An oil film with refractive index 1.48 and thickness 290 nm is floating on water and illuminated with white light at normal incidence. What is the wavelength of the dominant color in the reflected light?

Answer 1

Answer:

572.3 nm

Explanation:

$n_{oil}$ = refractive index of the oil film = 1.48

$t_{oil}$ = thickness of the oil film = 290 nm

$\lambda$ = wavelength of the dominant color

m = order

Using the equation

$2 n_{oil} t_{oil} = (m + 0.5) \lambda$

For m = 0

$2 (1.48) (290) = (0 + 0.5) \lambda$

$\lambda$ = 1716.8 nm

For m = 1

$2 (1.48) (290) = (1 + 0.5) \lambda$

$\lambda$ = 572.3 nm

For m = 2

$2 (1.48) (290) = (2 + 0.5) \lambda$

$\lambda$ = 343.4 nm

Hence the dominant color wavelength is 572.3 nm