Nonreflecting coating on a lens

[titan81]

Homework Statement

A transparent film (n = 1.6) is deposited on a glass lens (n = 1.76) to form a nonreflective coating. What is the minimum thickness that would minimize reflection of light with wavelength 500 nm in air?

Homework Equations

wavelengthXfrequency=c/n (Not sure if that's relevant)

The Attempt at a Solution

Not sure how to start. I'm having trouble with this problem. Can someone please help

 

[berkeman]

Homework Statement

A transparent film (n = 1.6) is deposited on a glass lens (n = 1.76) to form a nonreflective coating. What is the minimum thickness that would minimize reflection of light with wavelength 500 nm in air?

Homework Equations

wavelengthXfrequency=c/n (Not sure if that's relevant)

The Attempt at a Solution

Not sure how to start. I'm having trouble with this problem. Can someone please help

Welcome to the PF.

How do anti-reflection coatings on optics work?

 

[titan81]

I'm not sure. Thats my problem. I'm completely lost on this topic.

 

[turbo]

Have you Googled on anti-reflective coatings? Lens designers choose coatings and apply them such that internal reflections between individual elements of a lens are minimized, at least for the wavelengths that the sensor (human eye, chip, etc) can sense.

 

[rwisz]

me?

I can provide some insight into this problem. The concept of a nonreflective coating on a lens is commonly used in optics to reduce glare and improve image quality. In this case, the goal is to minimize the reflection of light with a wavelength of 500 nm in air.

To find the minimum thickness of the coating, we can use the equation for thin film interference: mλ = 2ntcosθ, where m is the order of the interference, λ is the wavelength of light, n is the refractive index of the coating material, t is the thickness of the coating, and θ is the angle of incidence. In this case, we are interested in the first order of interference, so m = 1.

Since we are working with a single wavelength of 500 nm, we can simplify the equation to t = λ/(2n1cosθ), where n1 is the refractive index of the lens material (1.76 in this case). We can also assume that the angle of incidence is 0 degrees, so cosθ = 1.

Plugging in the values, t = (500 nm)/(2*1.6*1) = 156.25 nm. This is the minimum thickness of the coating that would minimize reflection of light with a wavelength of 500 nm in air.

I hope this helps with your understanding of the problem. Keep in mind that this is a simplified solution and in reality, there may be other factors to consider such as multiple wavelengths of light and the angle of incidence.