Anti-Reflecting coatings on a glass lens

[BananaMan]

heres the question:

anti-reflection coatings on a glass lens (n=1.50) consists of a magnesium fluoride (n=1.38) film, the coating thickness is chosen to eliminate any back reflectionusing the ideas of destructive interference. What is the minimum coating thickness required to eliminate the reflection from a helium-neon laser at 632.8nm? Should the coating be the same thickness on both the front and rear faces of the lens?

really don't have a clue where to go with this one, looked all through my notes for this and can't find anything on coatings, if someone could just point me in the right direction i should be able to do it? thanks

 

[physicsprasanna]

thin film interference...

 

[kyle8921]

I can provide some insight into this question. Anti-reflective coatings are commonly used on glass lenses to reduce the amount of light that is reflected off the surface of the lens. This is achieved by creating a thin film with a different refractive index than the lens material. In this case, the coating consists of a magnesium fluoride film with a refractive index of 1.38, which is lower than the refractive index of glass (1.50).

To calculate the minimum coating thickness required to eliminate reflection from a helium-neon laser at 632.8nm, we can use the equation for the thickness of a thin film required for destructive interference:

t = (m + 1/2)λ/n

where t is the thickness of the film, m is the number of wavelengths in the film, λ is the wavelength of the incident light, and n is the refractive index of the film material.

For the helium-neon laser at 632.8nm, we can assume that m = 0 (since we want destructive interference). Plugging in the values, we get:

t = (0 + 1/2)(632.8nm)/(1.38)

t = 229.9nm

Therefore, the minimum coating thickness required to eliminate reflection from the helium-neon laser at 632.8nm is approximately 229.9nm.

As for whether the coating should be the same thickness on both the front and rear faces of the lens, it depends on the angle at which the light hits the lens. If the light is perpendicular to the lens, then the coating thickness should be the same on both faces. However, if the light is at an angle, then the coating thickness may need to be adjusted to achieve destructive interference. This can be calculated using the equation above, taking into account the angle of incidence and the refractive index of the lens material.

I hope this helps to guide you in the right direction. If you have any further questions, please feel free to ask.