Reflection of light off film, wavelength and thickness?

[mithraz87]

What is the thinnest film of MgF2 (n = 1.39) on glass that produces a strong reflection for light with a wavelength of 680 nm?

This is the exact question I am faced with. I didn't really know where to begin so I tried using the ratio of n-air/wavelength to n-film/(new wavelength) to try and find the original wavelength. I found that, and really didn't know where to go then. I have looked around, and I just can't seem to find anything. Any help would be greatly appreciated.

 

[alphysicist]

Hi mithraz87,

What is the thinnest film of MgF2 (n = 1.39) on glass that produces a strong reflection for light with a wavelength of 680 nm?

This is the exact question I am faced with. I didn't really know where to begin so I tried using the ratio of n-air/wavelength to n-film/(new wavelength) to try and find the original wavelength. I found that, and really didn't know where to go then. I have looked around, and I just can't seem to find anything. Any help would be greatly appreciated.

From your post, I was wondering if you asking what type of problem this is? This problem is dealing with the interference by thin film; I would think that your textbook has at least a section devoted to the topic with some examples.

You can also look at http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/thinfilm.html#c1

Does that help? If you are still stuck, post what you have tried.

 

[baba89]

I would approach this question by first understanding the basic principles of reflection and thin film interference. When light strikes a film, part of it is reflected off the surface while the rest is transmitted through the film. The reflected light waves can interfere with each other, leading to constructive or destructive interference depending on the thickness of the film and the wavelength of light.

In this case, we are dealing with a thin film of MgF2 on glass. The key information we have is the refractive index of MgF2 (n = 1.39) and the wavelength of light (680 nm). We also know that for strong reflection, we need constructive interference, which means the thickness of the film must be an integer multiple of half the wavelength of light.

To determine the thinnest film that would produce strong reflection at 680 nm, we can use the equation for thin film interference:

2nt = mλ

Where:
n = refractive index of the film
t = thickness of the film
m = order of interference (integer)
λ = wavelength of light

Since we want the thinnest film, we can assume m = 1. Rearranging the equation, we get:

t = (mλ)/(2n)

Substituting the values, we get:

t = (1 x 680 nm)/(2 x 1.39)

t = 245.3 nm

Therefore, the thinnest film of MgF2 on glass that would produce strong reflection at 680 nm is 245.3 nm thick.

Note: This calculation assumes that the film is surrounded by air. If the film is on a glass substrate, we would need to account for the refractive index of glass as well.