# Does humidity affect image formation point while observing through a telescope?

I was wondering if atmospheric humidity affects the point where an image forms through a telescope?

I have a 256mm aperture 1200mm focal length Newtonian Reflector. I generally use a 25mm eyepiece and get a sharp image with the focuser extended ~halfway. Recently, I was out observing when the atmospheric humidity was over 70%, and the temperature over 90F. I didn't get a sharp image even with the focuser extended fully. I fastened the eyepiece pulled out a little bit to get a fairly sharp image. Why could this be happening?

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This is a great question!

It's instructive to first look at refractor telescopes before considering your reflector.

### Refracting telescopes

Snell's law gives the relationship between the angles of incident and transmitted rays of light ($$\theta_1, \theta_2$$) at a boundary between two media (e.g. glass and air) of different indexes of refraction ($$n_1, n_2$$) as

$$\sin\theta_2 = \frac{n_2}{n_1} \sin\theta_1$$

and if the angles are small we can use the small angle approximation and replace $$\sin(\theta)$$ with \theta and get

$$\theta_2 = \frac{n_2}{n_1} \theta_1$$

This gives that the ratio of the two angles depends on the ratio of the two indices. So anything that affects the index of either medium (temperature, pressure, other materials mixed in, etc.) So adding water to the air will change its refractive index and therefore affect the focusing of a lens.

### Reflecting telescopes

As long as we approximate the behavior of a reflecting surface as a reflection exactly at the surface, we use the simple formula for specular reflection

$$\theta_2 = \theta_1$$

The approximation that reflection happens exactly at the surface can be applied both to Fresnel reflection at glass surfaces and metal surfaces.

So the simple and almost exactly correct answer to your question is "No".

### But wait, there's more!

This is a good opportunity to look a little deeper into the optics at surfaces.

It turns out that the phase shift upon reflection tells us that the light waves "spend a little time" inside the material and some amplitude penetrates to a small depth. It's only a few nanometers for metal (think conduction electrons and plasma frequency and skin depth) but it's on the scale of wavelengths for Fresnel reflection from dielectric surfaces.

Conjecture: I believe that you can prove this experimentally by reflecting a narrow gaussian beam of light off of a dielectric surface of higher index than air, and noting that while the angle of reflection is equal to the angle of incidence, the axis of the reflected beam, traced back to the intersection with the surface is offset slightly from the intersection of the incident beam axis with the surface, they actually meet at a depth of order a wavelength below the surface, which can all be derived from classical E&M theory.

Here's the problem with the above conjecture; I can't link to an authoritative source or derive it myself... yet. I hope that soon I will be able to find that reference and will be able to finally get to the bottom of the following in Physics SE (unless someone beats me to it!)

### And so, what is your point uhoh?

The point is that the effective reflecting surface is just slightly behind the physical surface, and that distance will depend ever so slightly on the matching of the fields at the boundary (i.e. boundary conditions). When the medium above the glass or metal reflecting surfaces has a different index, for example because the air is now humid, the effective reflecting surface will move ever so slightly.

This displacement would not be detectable or measurable directly as it is many orders of magnitude smaller than the depth of focus of the system, but if you had patience and an extremely precise ellipsometer you would be able to measure the change in relative phase shift upon reflection between two polarizations at oblique incidence and verify that I'm not as crazy as I sound :-)

• I agree with uhoh that the position of the focus is not going to change by many mm. I have never experienced a focus change like this regardless of observing at -5C to 35 C. Did you forget to tell us that you took something apart and put it back together improperly? Jun 22 at 2:46
• @JohnHoltz is "you" me or someone else?
– uhoh
Jun 22 at 7:33
• "You" was meant to be @shan42nd. Sorry, I should have made that more clear or split into two comments. The only explanation I would have for the movement of the focal point is if the primary mirror moved (as if removed for cleaning and re-installed in a different set of mounting holes) or the eyepiece changed. Both are a stretch (no pun intended). Jun 22 at 20:12
• Got it, thanks! the OP won't get a notification that you've made a comment for them unless 1) you use @shan42nd after they have already commented here, or 2) you leave it under the question. Otherwise they won't know you've commented if they read the answer before you did and then moved on.
– uhoh
Jun 23 at 0:35
• @JohnHoltz I did not take apart the primary mirror for any sort of cleaning. In fact right before I left for this particular observing session, I checked the mirror alignment with a collimator and it was perfect. Same case afterwards as well. Jun 23 at 18:57