A film of oil that has an index of refraction equalto 1.45 floats on water (n = 1.33). When illuminated by white light at normal incidence, light of wavelengths 629 nm and 449 nm is predominant in the reflected light. Determine the thickness of the oil film.

Question

A film of oil that has an index of refraction equalto 1.45 floats on water (n = 1.33). When illuminated by white light at normal incidence, light of wavelengths 629 nm and 449 nm is predominant in the reflected light. Determine the thickness of the oil film.

Wouldn't the thickness of the oil film be such that the thickness*2 be a whole multple of wavelengths?

http://physics.bu.edu/py106/notes/Thinfilm.html

Answer 1

To determine the thickness of the oil film, we can use the concept of interference in thin films. According to the given information, the oil film has an index of refraction of 1.45, while water has an index of refraction of 1.33.

In order for constructive interference to occur, the thickness of the oil film should be such that the path difference between the two reflected waves (from the top and bottom surfaces of the film) is equal to an integer multiple of the wavelength.

Let's consider the two wavelengths given in the problem: 629 nm and 449 nm.

First, we need to calculate the wavelength of light in the oil film. We can do this by dividing the given wavelength by the index of refraction of the oil:

Wavelength in oil = Wavelength in vacuum / Index of refraction of oil = 629 nm / 1.45 = 433.1 nm

and

Wavelength in oil = 449 nm / 1.45 = 309.7 nm

Now, let's consider the two possible scenarios:

For the constructive interference to occur at 629 nm, the path difference should be equal to an integer multiple of 629 nm in the oil film. In other words:

Path difference = 2 * thickness = m * wavelength in oil,

where m is an integer.

Similarly, for the constructive interference to occur at 449 nm, the path difference should be equal to an integer multiple of 449 nm in the oil film:

Path difference = 2 * thickness = n * wavelength in oil,

where n is an integer.

To find the thickness of the oil film, we need to find a common value for m and n that satisfies both conditions. We can do this by finding the common multiples of the wavelengths in the oil.

The common multiples of 433.1 nm and 309.7 nm are:

Common multiple = lcm(433.1, 309.7) = 133520.7 nm = 133.52 µm.

So, the thickness of the oil film should be:

Thickness = 133.52 µm / 2 = 66.76 µm.

Therefore, the thickness of the oil film is approximately 66.76 µm.