# Do antireflective coats increase the angle of total internal reflectio

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1. Oct 29, 2013

### Stargazer19385

And I mean the angle with the normal vector.

Suppose you shine a laser through a prism at a large angle of incidence, and the prism has index of refraction 1.7. You get the angle of incidence high enough, and you get total internal reflection. Then you put a 1/4 wavelength layer of MgF, index 1.38 on the face of the prism where the total internal reflection is occurring. Would the prism the let some light through, and then have the same total internal reflection angle that a pure MgF prism would have, allowing a higher angle with the normal?

I'm designing an eyepiece and trying to figure out just how much bending I can get away with. What if some nanoparticles are added on top of the MgF, giving a second layer of index 1.18? Would that allow significantly higher angles? Would the nano particles likely be uneven and cause scattering? Nikon claims to have that technology.

Last edited: Oct 29, 2013
2. Oct 29, 2013

### Drakkith

Staff Emeritus
I'm no expert, but doesn't total internal reflection depend on the difference between the to mediums' refractive indices? I would expect that adding a layer of something with a refractive index in between that of the two mediums would give you less of an angle. But I could be mistaken.

3. Oct 29, 2013

### Stargazer19385

That intermediate index is what I was basing my hope on. I just did not know if there was a certain thickness required in wavelengths for the light to register the intermediate layer. The layer is thick enough to reduce reflections from both sides of a piece of glass at zero incident angle, but I don't know how much it helps at non-normal angles. Wide angle eyepieces usually use 3 lenses to bend the light sufficiently, possibly for the purpose of avoiding high incidence angles, or possibly just to avoid manufacturing a highly curved lens. I wanted to do it in two lenses to reduce the total number of reflections.

4. Oct 29, 2013

### Drakkith

Staff Emeritus
Oh, I see what you're wanting to do.
Honestly, I'm not sure. Just going off the basics of what I know, it seems like it would work, however it could be that I have no idea what I'm talking about and that it's much more complicated than I think.

I can say that reducing the number of lenses will require that the remaining two have increased curvature, which means that aberrations will be higher and harder to correct.

5. Oct 30, 2013

### ehild

The product of the refractive index and the sine of the angle with the normal is the same in every medium:

Nisinαi=No sin(αo), where No and αo refer to air.

Let the angle in the prism be greater than the critical angle N2sinα2>1 (sinα2>0.588, α2>36°.
With a layer on the prism, the sine of the angle of the light inside the layer is sinα1= N2sin(α2)/N1, sinα1=1.7/1.38sin(α2) for the MgF2 film. If 0.588<sin(α2) <0.81, (36°<α2<54°) the light enters into the layer and reaches the layer-air interface, but will be totally reflected there, as

N1sinα1=N1(N2sin(α2)/N1) = N2sin(α2) >1. You can not avoid totalreflection at the end.

ehild

6. Oct 30, 2013

### Stargazer19385

http://refractiveindex.info/?group=PLASTICS&material=PMMA

I looked at the reflection graphs for different materials, including MgF, and found that as the index of refraction goes down, the angle with 5% reflection goes up a bit, but not as much as I would expect. Lowering the index of refraction just seems to shave 2% or so off across most angles. If 6% is acceptable, I might be able to get the 90 degree apparent FOV I want. The nice thing is the reflection will be angled up at the walls instead of the other lenses. I would just need to make sure that light is absorbed. Maybe put some MgF nano particles on the black walls with baffles too.

7. Oct 30, 2013

### Cthugha

You cannot avoid it if you insist on parallel surfaces. One solution to modify the effective critical angle lies in putting some thicker specially shaped second material instead of a thin ar-coating layer on the prism.

I have seen people putting hemispheres directly on a sample inside a cryostat to modify the effective limiting angle of total internal reflection. You cannot change the limiting angle between the beam and the normal at the hemisphere-air interface, but by using a hemisphere you can make sure that there is no angle between the beam and the surface normal.

8. Oct 30, 2013

### Stargazer19385

By parallel surface, I think you mean plano surface, such as the plano back side of an convex plano lens where the bent rays hit it at a non zero angle on the way out, which is more angle sensitive than the way in. Carving the back side to be spherical concave, with a radius of curvature such that all the out going rays are normal to the surface, not only increases transmission and reduces reflections, but also reduces chromatic aberration.

I still have to get by the high angle of the low f# lens's convex surface. The consensus seems to be that a thin AR coating will not change the maximum allowed angle, or not by much.