Probelm with fringes/interference

[rooseallie]

Homework Statement

Basically I have a thin film that I know is 20nm and I want to verify its thickness. I use a laser that is 632.8nm, angle of incidence is 45 degrees, refractive index of the film is 1.95, fringe spacing is roughly 1.5mm, and I have 6 bright fringes on the screen that is 25cm away from the sample that the light is scattered off.

Homework Equations

I tried the usual m*lambda = d*sin_theta and nothing works out. I would like to calculate it in terms of the fringe spacing

The Attempt at a Solution

i used another formula: d = m/2Dm*sqrt(n^2 - sin^2_thetha) where m is the number of fringes in the wavenumber region Dm, which is calculated from dm = 2*pi/lambda.

any help is greatly appreciated! Allie

 

[mark726]

Hello Allie,

Thank you for sharing your experiment and the equations you have tried. It seems like you are on the right track, but there are a few things to consider in order to accurately calculate the thickness of your thin film.

Firstly, it is important to note that the equations you are using assume that the light is passing through the film, rather than being reflected off of it. Since you are using a laser and measuring the fringes on a screen, I assume that the light is being reflected off the film. In this case, the equations you have used will not give you an accurate result.

To calculate the thickness of a thin film using reflected light, you can use the equation d = m*lambda/2n, where m is the number of fringes, lambda is the wavelength of the light, and n is the refractive index of the film. However, this equation assumes that the angle of incidence is 0 degrees. Since your angle of incidence is 45 degrees, you will need to use the equation d = m*lambda/(4n*cos(theta)), where theta is the angle of incidence.

In addition, it is important to make sure that you are using the correct value for the refractive index. The refractive index can vary depending on the wavelength of the light, so make sure you are using the correct value for the 632.8nm laser.

Lastly, it is important to consider the units of your measurements. In your post, you have given the fringe spacing as 1.5mm, but the distance to the screen as 25cm. Make sure to use consistent units in your calculations.

I hope this helps you in calculating the thickness of your thin film. Let me know if you have any further questions. Good luck with your experiment!