# Anti-reflective coating optimum index of refraction

• reb30
In summary, the conversation is about trying to find the optimum index of refraction for an antireflective coating on a piece of glass. The equation n1=sqrt(n0ns) is mentioned, but the participants are having difficulty deriving it and finding resources that explain it. One participant suggests checking the textbook "Optics" by Hecht's for a derivation, but it is complicated and not specifically for normal incidence.

#### reb30

Hello

I'm trying to solve a problem where I'm asked to find the optimum index of refraction for an antireflective coating on a piece of glass. In trying to derive an equation for it I keep coming across this in the internet (where 1,0, and s should be subscripts)

n1=sqrt(n0ns)

where n1 is the index of refraction of the coating, n0 is that of the air, and ns is the glass (see here - http://en.wikipedia.org/wiki/Antireflection_coating) [Broken]. I can't work out how this was derived for the life of me and can't find it anywhere in books or the internet. Does anyone have any ideas?

Thanks a lot

Robert

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I also have found this near impossible, despite spending hours working on it. My books quote that the relation given above should give zero reflection, but the only way I can make that happen is if n0 = ns.

I understand theoretically how and why this should work, I just can't get it to work mathematically..

@reb30:

I don't know if you own a copy of the textbook "Optics" by Hecht's but there's a derivation on page 375. Unfortuanatly it's very complicated and is done for general angle of incidence, rather than normal incidence. I couldn't make it work for simplified start conditions..

## 1. What is an anti-reflective coating?

An anti-reflective coating is a thin layer of material that is applied to the surface of an object, such as a lens or window, to reduce the amount of light that is reflected off of it. This helps to improve the clarity and visibility of the object by allowing more light to pass through it.

## 2. How does anti-reflective coating work?

Anti-reflective coatings work by using the principle of interference to reduce the amount of light that is reflected off of a surface. The coating is designed to have a specific thickness and refractive index, which causes incoming light waves to cancel each other out, resulting in less reflection.

## 3. What is the optimum index of refraction for anti-reflective coating?

The optimum index of refraction for anti-reflective coating depends on the material it is being applied to and the wavelength of light being used. Generally, a refractive index of around 1.4 to 1.5 is considered to be ideal for most applications.

## 4. What are the benefits of using anti-reflective coating with the optimum index of refraction?

Using anti-reflective coating with the optimum index of refraction can provide several benefits, including improved clarity and visibility, reduced glare, and increased light transmission. It can also help to protect the surface of the object from scratches and other damage.

## 5. How is the optimum index of refraction for anti-reflective coating determined?

The optimum index of refraction for anti-reflective coating is determined through a combination of mathematical calculations and experimental testing. Factors such as the material of the surface, the desired level of reflection reduction, and the wavelength of light being used are taken into account to determine the best refractive index for the coating.