# Reflectivity coefficient of a composition of layers

• LCSphysicist
In summary, the conversation discusses the placement of a Ti02 film with an index of 2.5 on top of glass with an index of 1.5 to increase reflection in the visible spectrum. The question then asks for the desired thickness of the film in microns and the resulting reflectivity. The concept of reflectivity is defined and the answer is given as ##r=(\frac{n_0 - n_1²/n_2}{n_0 + n_1²/n_2})^2##, which may contradict the author's previous statement about wanting to decrease the intensity of the reflected wave. The conversation also mentions the possibility of an odd number of traversals of the film, but no clear answer is provided
LCSphysicist
Homework Statement
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Relevant Equations
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> A Ti02 film of index 2.5 is placed on glass of index 1.5 to increase
the reflection in the visible. Choosing a suitable value for wavelength, how
thick a layer in microns would you want, and what reflectivity would this
give you?

My question is about the last question presented above. Precisely, i am having some trouble to understand what it means by "reflectivity", i guessed that it is the coefficiente R that points the intensity obtained from a reflection, in this case normal, so generally ##r_{12}=(\frac{n_1 - n_2}{n_1 + n_2})^2##. In this case, i thought that, since we want to increase the reflection and at the same time decrease the intensity, the reflected wave need to be out of phase by pi and the reflectivity would be ##|r_{10}-r_{12}|##, where 0 is the air, one is the film and two is the glass.

But, the answer is ##r=(\frac{n_0 - n_1²/n_2}{n_0 + n_1²/n_2})^2##, i have no idea how does the author got this answer. Any help?

The answer to the first part is any multiple of half a wavelength, right?

For the second part, I have trouble believing the given answer. It says that if ##n_1^2=n_0n_2## then there's no reflection.
You don't explain how you got your answer. Did you take into account a reflected ray can undergo any odd number of traversals of the film?
I get ##1-\frac{4n_0n_1n_2}{(n_0+n_2)(n_0n_2+n_1^2)}##, but not confidently.
(Without this comment, Latex seems to lose a subscript 1 at the end there. With this comment it’s fine!)

## 1. What is reflectivity coefficient?

The reflectivity coefficient is a measure of the amount of light that is reflected off of a surface. It is usually expressed as a percentage and can range from 0% (no light reflected) to 100% (all light reflected).

## 2. How is the reflectivity coefficient calculated?

The reflectivity coefficient is calculated by dividing the amount of light reflected off of a surface by the amount of light that is incident on the surface. This calculation takes into account the angle of incidence and the properties of the surface material.

## 3. What is a composition of layers?

A composition of layers refers to a structure that is made up of multiple layers of different materials. These layers can have varying thicknesses and properties, and they can be stacked on top of each other to create a specific structure or material.

## 4. How does the composition of layers affect the reflectivity coefficient?

The composition of layers can greatly affect the reflectivity coefficient of a material. The thickness, refractive index, and absorption coefficient of each layer can impact the overall reflectivity of the material. Additionally, the order and arrangement of the layers can also play a role in the reflectivity coefficient.

## 5. Can the reflectivity coefficient of a composition of layers be controlled?

Yes, the reflectivity coefficient of a composition of layers can be controlled by adjusting the properties and arrangement of the layers. By carefully selecting the materials and thicknesses of each layer, the overall reflectivity of the material can be tailored to meet specific needs or applications.

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