Question

White light is shone perpendicularly onto a film of unknown thickness, with index of refraction n=1.5.

a) How thick would the film have to be for each of the following colors of light to be absorbed due to destructive interference?

Red (f= 4 x 10^14 Hz)

Green (f= 5.45 x 10^14 Hz)

Blue (f= 6.38 x 10^14 Hz)

b) Draw a ray diagram that indicates the path of the red light from part a) into and out of the film and justify the fact that red will not be seen in the reflected light.

Answer 1

a) Wavelength of the given light will be:

So for Red light, the wavelength is: 750 nm

Similarly for green, the wavelength is: 550nm and Blue light is 470nm

For destructive interference, the path difference between the waves reflected from upper and lower edges should be half of the wavelength.

For normal incidence,

Here, n = 1.5

So, for Red light, the minimum thickness will be:

t = 125nm

For green light, t = 91.66 nm and for blue light, t = 78.33nm.