The table lists the range of wavelengths in vacuum corresponding to a given color. If light one illuminates a film that has a refractive index of 1.333 and thickness of 183 nm with white light, which color is missing from the light reflected from the film?
A)red
B)yellow
C)blue
D)green
E)orange

Question

The table lists the range of wavelengths in vacuum corresponding to a given color. If light one illuminates a film that has a refractive index of 1.333 and thickness of 183 nm with white light, which color is missing from the light reflected from the film? 
A)red 
B)yellow 
C)blue 
D)green 
E)orange

Quizplus · Accepted Answer

When light passes through a film with a refractive index n and thickness t, there is a phase shift of π between the reflected light waves. For constructive interference to occur, the path difference between the reflected waves must be an integer multiple of the wavelength λ in the film medium. The wavelength of light in the film can be calculated as λ = λ_0/n, where λ_0 is the wavelength in vacuum.

Using the given wavelengths in vacuum for the different colors, we can find their corresponding wavelengths in the film:

Red: 620-750 nm → 465-562 nm in the film
Orange: 590-620 nm → 443-465 nm in the film
Yellow: 570-590 nm → 428-443 nm in the film
Green: 495-570 nm → 371-428 nm in the film
Blue: 450-495 nm → 337-371 nm in the film
Violet: 380-450 nm → 285-337 nm in the film

The thickness of the film and the refractive index of the film only affect the wavelength of light in the film, not the range of wavelengths in vacuum for each color. Therefore, we can see that blue light has the shortest wavelength in the film, and thus it is the most likely color to be missing from the reflected light. Therefore, the correct answer is C) blue.

The Table Lists the Range of Wavelengths in Vacuum Corresponding