Finding the Minimum Thickness for Destructive Interference in Thin Films

[Sofija Zdjelar]

Homework Statement

A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread uniformly over the surface of crown glass of refractive index 1.52. Light of wavelength 515 nm falls at normal incidence onto the film from air. You want to increase the thickness of this film so that the reflected light cancels.

What is the minimum thickness of TiO2 that you must add so the reflected light cancels as desired?

Homework Equations

Am i using the wrong formulas? The examples in my book seem to solve these kind of exercises easily... How should i solve this exercise?

The Attempt at a Solution

I have used the formula for destructive reflection from thin film, half-cycle phase shift (2t = mλ with λ = λ_air/n_film). However, it is not correct. I have also tried to use the formula for destructive reflection from thin film, no relative phase shift ((2t = m + 1/2)λ), which also did not work. I have mainly used m = 1 because i read somewhere that it is 1 when calculating the minimum thickness.

 

[TSny]

Hello and welcome to PF.

If you put the original value of the thickness of the film into the formula 2t = mλ, what would you get for m? Do you get an integer?

 

[Sofija Zdjelar]

Hi! Thank you for answering. No, i do not get an integer...

 

[TSny]

Hi! Thank you for answering. No, i do not get an integer...

OK. So, that means the original thickness of the film gives neither constructive nor destructive interference. As you increase the thickness of the film beyond the initial thickness, what would be the first value of m for which you would get destructive interference?

 

[Sofija Zdjelar]

I get m = 11 (when i use the formula 2t = mλ and λ being λ_air/n_film
Not sure if 11 is correct, or what I am supposed to do with it.

 

[TSny]

I think m = 11 is right. What is the thickness of the film that corresponds to m = 11? How would you use this to answer the question?

 

[Sofija Zdjelar]

The thickness that corresponds to that m is 1081, which means that i have to add 45 nm to the existing film. I tried it and it was right! Thank you so much :-)

 

[TSny]

OK. Good work.