A film of gasoline (n=1.40) floats on water (n=1.33). Normally incident blue light of a wavelength 480 nm, appears bright blue due to constructive interference. Determine the minimum non-zero thickness of the film
waves reflected from the gasoline/water interface
... are in phase with the incident light
this means the minimum film thickness is half a wavelength
so which formula should i use?
To determine the minimum non-zero thickness of the film, we need to analyze the concept of constructive interference and the conditions required for it to occur.
Constructive interference occurs when two waves combine to form a wave with a larger amplitude. In the case of thin films, constructive interference happens when the reflected light from the top surface of the film interferes with the light reflected from the bottom surface of the film.
The condition for constructive interference is given by the equation:
2t = mλ / (n_film - n_medium)
Where:
- t is the thickness of the film
- m is an integer representing the order number (m = 0, 1, 2, ...)
- λ is the wavelength of light in the medium (in this case, 480 nm)
- n_film is the index of refraction of the film material (1.40 for gasoline)
- n_medium is the index of refraction of the medium (1.33 for water)
We want to find the minimum non-zero thickness, which corresponds to the first constructive interference condition (m = 1). Plugging in the values, we have:
2t = (1)(480 nm) / (1.40 - 1.33)
2t = 480 nm / 0.07
t = (480 nm / 0.07) / 2
t = 3428.57 nm / 2
t = 1714.28 nm
Therefore, the minimum non-zero thickness of the film is approximately 1714.28 nm.