Destructive interference of light

[abohn1]

White light is shined 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? (15 points)

Red (f = 4 * (10^14) Hz)
Green (f = 5.45 * (10^14) Hz)
Blue (f = 6.38 * (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.


This online physics class blows me away at the homework questions it asks because it does not explain anything thoroughly. Wondering if someone could guide me in right direction, maybe which equation is best used here?

 

[jbsteele]

A. The thickness of the film needed for each color of light to be absorbed due to destructive interference can be found using the equation for wavelength, λ = c/f, where c is the speed of light and f is the frequency of the light. The thickness, d, of the film can be found by rearranging the equation to get d = λ/(2n). For red light (f = 4 * (10^14) Hz): d = (3*10^8)/(2*1.5*4*10^14) = 0.0015 m. For green light (f = 5.45 * (10^14) Hz): d = (3*10^8)/(2*1.5*5.45*10^14) = 0.001 m. For blue light (f = 6.38 * (10^14) Hz): d = (3*10^8)/(2*1.5*6.38*10^14) = 0.0008 m. B. The ray diagram should show a wave of light entering the film, being split into two waves by the film, and then the two waves recombining with 180 degrees out of phase with each other. The resulting wave is then reflected off the film, and the two waves pass through each other, canceling out the red light from the reflection.