Oil film thickness for total reflection 500nm

[messick11]

Homework Statement

I was asked to determin the film thickness for an oil film (n=1.33) for a light beam (500 nm) to give total reflection. I could calculate refraction angle for air to oil, but have no idea as to how to approach this question.

Homework Equations

The Attempt at a Solution

 

[technician]

This is an interference question. Light reflected from the front surface of the film interferes with light reflected from the back surface. For total reflection the 2 reflected waves must be in phase.
Points to consider
1) at the air/film surface a phase change of π (λ/2) occurs (there is no phase change at the film/air surface)
2) In the film the light travels a distance = 2 x thickness of the film and the wavelength changes.

Hope this gets you started !

 

[messick11]

Thank you VERY much. I never thought of it as an interference problem!

 

[technician]

Its a pleasure. Did you get 94nm (λ/4 for the wave in the oil)?

 

[paranormal]

Total internal reflection occurs when the angle of incidence of a light beam is greater than the critical angle, which is determined by the refractive indices of the two mediums involved. In this case, the two mediums are air and oil, with the refractive index of oil being 1.33.

To calculate the critical angle, we can use the equation:

sinθc = n2/n1

Where θc is the critical angle, n2 is the refractive index of the second medium (in this case, oil), and n1 is the refractive index of the first medium (in this case, air).

Plugging in the values, we get:

sinθc = (1.33)/1 = 1.33

Taking the inverse sine of both sides, we get:

θc = 49.35 degrees

This means that for total internal reflection to occur, the angle of incidence of the light beam must be greater than 49.35 degrees.

To determine the film thickness for total reflection, we need to consider the path of the light beam as it enters and exits the oil film. If the light beam enters the oil film at an angle greater than the critical angle, it will undergo total internal reflection and continue to travel through the oil film without being refracted. This means that the thickness of the oil film will not affect the total reflection.

Therefore, the film thickness for total reflection in this case would be any thickness that allows the light beam to enter and exit the oil film at an angle greater than the critical angle, which we have determined to be 49.35 degrees.