everyday-lifeoptics
I am gazing through my office window into a heavy rain. I am thinking that raindrops are like small lenses that bend the light. Thus I am surprised, that I can clearly see other buildings through the window.
So, why is it that we can see through the rain? Is the density of raindrops simply too low?
This is a real effect, but it doesn't have anything to do with coma or any of the optical aberrations. It is caused by the fact that the effective focal length shortens as you tilt a lens. When your eyesight gets worse, you need a stronger focal length lens in your eyeglasses, and tilting the lenses has this effect. The problem with doing this all of the time is that it introduces distortions such as the coma you've pointed out in your question.
This presentation and this journal paper show the the effective focal length of a tilted lens from ray tracing simulations and from theory respectively. From the paper, the focal length for the tangential focal point (up and down as you look through your glasses) and the sagittal focal point (left and right as you look forward) are given from the paper by
$$
\begin{align}
f_{tan}&=f_0\frac{n-1}{n}\frac{\cos\theta\sqrt{n^2-\sin^2\theta}}
{\sqrt{n^2-\sin^2\theta}-\cos\theta}\\
f_{sag}&=f_0(n-1)\frac{1}{\sqrt{n^2-\sin^2\theta}-\cos\theta}
\end{align}
$$
where $n$ is the index of refraction of the material and $f_0$ is the original focal length. I've plotted $f/f_0$ for both of these in the figure below for an index of refraction of 1.5. I believe that this is special to a lens which has equal radii of curvature on both sides (bi-convex or bi-concave), but the results for other types of lenses will have similar outcomes.
Your inability to see the dust until you narrow the slit has nothing to do with the narrowness of the beam but instead the dynamic range of light that your eye can see at one time.
A bit of searching turns up reports of a contrast ratio for you eye at one time as between 100:1 and 1000:1. This means if you're in a room with a range of brightness greater than about 100 to 1 the brightest things will all be washed out as white and the darkest things will all be essentially black. This is obvious in photos that are "backlit" like this one:
These horses aren't black but because the ratio of the bright light to the dark horses exceeds the dynamic range of the camera the sky is washed out white and the horses are in silhouette.
Your eye can adjust over time to a huge range but it can't utilize the whole range all at once.
In the case of dust reflecting light, if you allow a lot of light into the room the relative brightness between the small amount of light the dust is reflecting and the rest of the illuminated room prevent you from seeing the dust.
This is fundamental to signal processing. Why can't you hear a whisper in a noisy room? The noise of the crowd obscures the whisper. The difference between the signal you're trying to pick up and the background noise is called the signal-to-noise ratio. In the case of dust, the light let into the room is scattered and reflected in the room and causes the room to be illuminated. This is the noise that obscures the signal from light reflected off of the dust.
Best Answer
Many of the photons coming from nearby objects will travel to your eye without striking a rain drop. However, photons traveling from more distant objects have a greater chance of hitting a rain drop before reaching you. This makes more distant objects seem dimmer or more difficult to see.