How was this amount of zoom created by the water droplets on the concave lens of my glasses?
First, the typical magnification one gets from a drop of water is only a factor of ~4-5, not 10s to 100s. It is possible to construct micro-lenses from water droplets as discussed here https://www.nature.com/articles/ncomms14673, however that wasn't done to generate high magnification but rather to focus light from individual locations with a high spatial resolution.
...a single cell was zoomed in to the level where I could see the nucleus in the center, some squiggly organelles outside the nucleus and an irregular cell membrane around it.
Are you sure what you saw wasn't within or on the water droplet? There are lots of smallish bugs/animals in water and on your face/glasses that could be magnified by a water droplet. Since you state the source of the water was rain, it's more likely the small critter was already on your glasses (glasses can be rather nasty afterall).
There are lots of micro-animals like tardigrades, myxozoans, rotifers, nematodes, and loriciferans, many of which can look like a cell. I would guess this is a much more likely explanation than a single water droplet actually generating microscope-level magnification allowing you to see single cells, which are on the micron scale.
It is not possible to take a picture of this phenomenon. Probably the cells are in my eye.
This is unlikely. The amount of light that is reflected off of a water droplet vs transmitted is low (e.g., see https://en.wikipedia.org/wiki/Electromagnetic_absorption_by_water), which is why you can see through them.
It is possible you have some small organisms in your eye, but that the water droplet provides a magnified reflected image is unlikely. The most likely answer is the one I propose above, namely, that there are micro-animals on your glasses that are being magnified by the water.
The maximum angular resolution (e.g., see visual acuity) of the human eye is ~0.47 arc minutes or ~28 arc seconds. Typically ~1 arc minute is considered to be good vision. The smallest objects resolvable by the human eye are limited by the diffraction limit of the pupil and come in around the width of a typical human hair or ~55-75 micrometers (e.g., see https://en.wikipedia.org/wiki/Naked_eye).
So if we use the magnification of ~4-5 I mentioned above, something that is acutally ~0.055-0.075 mm in size would appear to be ~0.22-0.30 mm through an ideal water droplet. To put it another way, assuming the above and ideal conditions, the smallest resolvable objects through a water droplet would be ~0.011-0.015 mm.
With all that in mind, I note that the size range of single-celled organisms is rather large. There are bacteria that have cell diameters of less than a micron while some protozoans can be more than 100 microns.
Thus, in principle, it is possible that a large, single-celled organism was magnified and visible to your naked eye through the water droplet and your glass lense. However, I still maintain the more likely explanation is that there were some micro-animal-like critters on your glasses that were magnified by the water droplet.
Side Note
Depending on where you live in the world can also influence whether there is a significant probability of small micro organisms existing within the water drops from rain fall, i.e., they are inside the rain drops before they hit the ground. So I initially argue this is less likely above, it is not impossible for the rain water itself to contain micro organisms, e.g., see https://www.nature.com/articles/s41545-019-0030-5.
When the surrounding temperature decreases, the water in a pond cools down starting from the top.
As long as the temperature of the water at the top is above $4^{\circ}$C, i.e., as long as its thermal expansion coefficient is positive, it becomes denser than the warmer water immediately below it and it sinks. The same process takes place at all levels - all the way to the bottom.
But, at some point, the temperature at the top will drop below $4^{\circ}$C. What happens next? Will the process described above continue?
Best Answer
You asked two questions; I am going to give a very long answer. But the TL;DR is:
As posed in the title: "Was Titanic's captain's decision correct?" - the answer is "probably yes"
As posed lower down: Was there a chance of Titanic to escape from its tragic fate?:- the answer is "once they had hit the iceberg the way they did, no".
The Titanic was considered "unsinkable" because any four of the sixteen compartments could be flooded and she would still float. These compartments (see picture below) were basically vertical "walls" throughout the ship. If the region between any two walls flooded, the water could not flow to the other compartments (when the flood doors were closed). Think of it as 16 smaller boats welded together and you get the idea.
However, when you look at the diagram you will see that these "walls" didn't reach all the way to the top. The ship's designer was on board for the maiden voyage, and he told the captain that she would not survive - losing more than 1/4 of the buoyancy was just too much, and as the ship started to list water would start to flow over the watertight barriers, filling compartment 6, 7, ... So closing the doors would not have helped. They key was to get passengers off the boat - at which they did a terrible job (not only did they not have enough life boats, but the ones they had were not all filled because there had been really no proper training - after all, she was "unsinkable").
If they had not tried to avoid the iceberg, but had instead hit it head-on, then they would have destroyed the front compartment (maybe even two); but they could have closed the watertight doors, and the ship would have survived. The bottles on the shelf in the first class bar might not have because the impact would have thrown everything and everyone around quite badly.
For more details see this which is also source of this image:
The tragedy was that by attempting to avoid the collision they scraped the iceberg (most of which was underwater - there's the physics bit) and it cut open five consecutive compartments (actually - the force of the collision popped the rivets). This led to a lack of buoyancy which caused the ship to tilt - and the flooding water ended up above the level of the watertight compartments (which didn't go all the way to the top) so other compartments could flood.
It is probably true that leaving the watertight doors between compartments open slowed the process of tilting. Once the ship reached a certain angle, stresses became too large (bending force from the front trying to sink and the back trying to float). It is believed that the boilers (remember this was a huge steam ship) broke loose and "fell" through the length of the ship, punching a hole as they picked up speed. The hull may also have snapped in half as the bending stresses were far greater than she was designed to withstand. At this point, the electricity generators failed, the hole in the hull became massively bigger, and the whole thing was over in seconds.
Source: My recollection from reading "A Night to Remember"
I just realized I am writing this on the 102nd anniversary of the sinking... That may be why you just saw the documentary.
UPDATE
The question "what if they had not tried to steer away" was still lingering in the back of my mind. Here is what I know:
So now we can do some math.
First question:
What kind of deceleration could they achieve with their engines hard astern?
Given $v=10.8m/s$ and $t=195s$, deceleration was $v/t=0.055 m/s^2$
Second question:
If they had thrown the engines full astern with 900 feet to go, how fast would they have been going on impact?
With $d=274m$, $v_{init}=10.8m/s$ and $a=-0.055m/s^2$, $v_{impact}=9.3m/s$
Note - that is the speed you would go if you dropped approximately 4.4 m, or jumped from the second storey of a building. Ouch.
Third question:
If they had reacted 37 seconds earlier, what would the answer be?
We subtract $at$ from the original answer and get $9.3 - 0.055*37 = 7.2m/s$. This corresponds to a drop from 2.6 m - a bit more than half the height from the previous answer.
Final question:
How much would the ship have crumpled with that kind of impact?
That's a tough one. The hull was made of 1 to 1.5 inch thick steel plates that were riveted together (and in fact it's the rivets popping that created the fatal hole in the hull). With a mass of over 53,000 tons (depends who you ask - they were going through 600 tons of coal per day so that number changed very quickly; but we're doing physics here so $5.3x10^7 kg$ is close enough) it had a momentum of $$9.3 * 5.3 * 10^7 = 4.9*10^{10}Nm$$
<briefly switching to imperial units. I'll be right back>Now the yield strength of steel is "around 40,000 psi", and let's assume that only the part of the ship below the waterline is involved in the collision. With a draft of 34 feet, and estimating the bow section to be 32 feet wide, we have approximately 100 linear feet of steel, or 1200 linear inches of steel. But these plates will have had considerable reinforcement, and bending that much steel would require a lot of force. But then Titanic had a lot of momentum...
<back to SI units>Consulting http://dspace.mit.edu/bitstream/handle/1721.1/77770/47046428.pdf , it is clear that the full calculation is quite complex - but photos in that thesis give us the general idea that the distortion might be "of the order of" 1/3 the height of the ship. That would be around 10m. If she did in fact come to a complete stop in 10 m, this would have required an acceleration of about 0.7g . So yes, there would have been casualties, especially among the fine china. Losing the front 10 m would have destroyed one compartment - but only one.
I suspect that a lot of ice would have been broken too - after all, the yield strength of ice is quite low compared to steel (at least 15x, although the values vary tremendously). But then the hull was "hollow" so as soon as the bow penetrated more than a couple of feet, the ice would win.
Would the iceberg have moved? With 9/10 of its volume below the surface, and with the iceber height comparable to the height of the ship, I am going to venture "not really" without attempting to do the detailed calculation.
Finally the question of the third propeller:
The third propeller was mounted in line with the rudder.
In such a configuration, when the propeller is thrusting forward, the water flow past the rudder and enhances the action of the rudder. When you "throw the engine in neutral" as was done just before the collision, the rudder is quite a bit less effective, and the ship will turn more slowly. In the extreme case, if you could reverse the thrust on the central propeller you would have to turn the wheel the other way to get the same turning effect.
Large modern vessels have a "bow thruster" - this is a turbine that is mounted transversely near the bow, and that allows lateral force to be applied regardless of the speed of the vessel. This allows for far greater maneuverability on these long ships - much more than "one forward one reverse" could ever do (just think about the difference in the arm of the force).
Another interesting reference:
physics world
I do have one lingering question in my own mind: when a sailing boat is slightly damaged in a collision, one will sometimes "keel haul" a sail - essentially pulling it underneath the hull so that it covers the hole and slows the rate at which water enters. I wonder whether Titanic had enough rope and cloth (and maybe steel plates) on board that a clear-thinking engineer might have carried out a similar emergency repair on the water. After all, it wasn't really necessary to stop the water from entering: it just needed to be slowed down enough to give the pumps a fighting chance; that said, the initial rate of flooding was 12x greater than the capacity of the pumps - so any "patch" would have had to be really quite good...
And one more excellent reference (contains discussions of much of the above in a lot more depth, and probably by more qualified people) is http://www.encyclopedia-titanica.org/ . I hesitate to post it because I only just found it, and it doesn't always agree with my analysis... I may have to write another update after I have digested some of its contents.