Physics of Rainbows; Moonbows; Fogbows - All You Need to Know - an Outreach Feature for the Community

Blog Contents and Who am I?

"The rainbow is one of the most beautiful phenomenon in nature. It has inspired art and mythology in all people and (to describe) it has been a pleasure and challenge to mathematical physicists..."  ...Vande Hulst

Rainbow is a bow-shaped display in the sky of the colours of the spectrum, caused by the refraction, reflection and dispersion of the Sun's rays through rain and mist.  ...Colin's English Dictionary 

The first satisfactory explanation of the formation of rainbows was given by Rene Descartes in 1637 based on the laws of reflection and refraction as enunciated by Snell in 1621.  That white light consists of rainbow colours was not known at the time. Isaac Newton subsequently explained the colours of the rainbow. 
Newton's explanation of the colours of the rainbow horrified poet John Keats.  Keats complained that by reducing the rainbow to its prismatic colours, Newton had robbed these marvels of nature of their magic. 

The magical rainbow  -  bright, elusive and heavenly -  is overpowering in its presence and has featured in mythology in all ancient societies.  Without the scientific tools, historic man described the rainbow with awe and inspiration. Rainbows are often portrayed as bridges between people and supernatural beings.  The mythologies developed around the rainbow are absolutely fascinating - I use slides 1 and 2  to describe some of them. You can look at 1, 2, 3 for many more.
The reason I decided to write a blog about rainbows is because, over the years many people have asked me how rainbows happen.  It is a subject people are curious about. The difficulties in explaining how rainbows are formed to somebody with no science background are obvious - I felt that it better to provide a detailed analysis with the basics written down too.  Such an analysis is not available in published literature at one place.  Because the blog is prepared as an outreach piece, I have repeated myself on few occasions  - just to make sure that the pace is not too quick.  Hope this works.  First I list the contents of the blog which are along the lines that people have asked me questions on this topic.

CONTENTS

Rainbows in Mythology

The Primary Rainbow (1st Order Rainbows)

At What Angle in the Sky is a Rainbow Seen?

Background Physics (may be skipped w/o loss of continuity)

Rainbow Formation for a Single Colour

Rainbow Formation with White Light

Why is Red at the Top of the Primary Rainbow?

Why is Sky Brighter Under the Primary Rainbow Arc?

Why is there a Dark Region Between the Rainbows?

The Secondary Rainbow (2nd Order Rainbows)

Rainbows and Water Drop Size

Higher Order Rainbow

Final Word

Click on the slide to view its full page image, press Escape to return to Text

Slide 1:

Slide 2:

The Primary Rainbow

In most cases, we see one rainbow - we call it the primary or 1st order rainbow and it is formed by one internal reflection inside of the raindrops. Standing on solid ground the rainbow we see is part of a circle.  From a high mountain or from a flying plane, sometimes it is possible to see the full circle of the rainbow.  
At times, you can see a second rainbow (secondary rainbow) that is at a higher elevation and is formed by two internal reflections within the raindrops. The two slides show such rainbows in their splendid beauty.
Slide 3:

Slide 4:

At what angle in the sky is a Rainbow seen?   

First we look at rainbow formation for light of one colour - monochromatic light. Myriads of raindrops are formed in rain clouds, and if in another part of the sky the Sun is shining, then parallel rays of sunlight will fall on the raindrops.  If you stand with your back to the Sun then the situation will be as in the diagram - a rainbow is observed when the raindrop deflects the incident rays from the Sun by 138 degrees. 

Slide 5:

Slide 6:

Slides for Background Physics

The science behind the formation, colours and structure  of rainbows requires some background in the way light propagates in different media - air and water in our case. Many of you would be familiar with this science - however, for completeness of description I have included some slides to explain these.  You can miss the next four slides (#7 to 10) - if you are familiar with Snell's laws of reflection and refraction of light.
Slide 7:

 Slide 8:

 Slide 9:

 Slide 10:

Rainbow Formation with a Single Colour  

Light rays of different colours behave differently at the boundary of two media.  First we analyze what happens to a single colour (monochromatic light) and then generalize how different colours disperse to form a rainbow when white light passes through raindrops.
Slide 11 follows the light ray as it enters a raindrop at point A, reflects at the back of the drop at B and then emerges at C in a direction that is different from its original direction.  The deflection angle d depends on the angle of incidence i and the refractive index n; dependence of d on i for water is plotted in slide 12. 
Slide 11:

 Slide 12:

The deviation of the direction of the incident ray passes through a minimum  for an incidence angle of 60 degrees and then d is 138 degrees.  From the figure in slide 12 we also notice that rays for i from about 50 to 70 degrees are bunched around 138 degrees and will emerge from the raindrop along 180-138 = 42 degrees relative to the original rays of light  - this is shown in slide 14.
Slide 13:  

 Slide 14:

Slide 14 shows that a lot more intensity is concentrated around the minimally deviated  ray (number 7 in slide 14) and if you look towards the raindrops along this direction (180 - 138 = 42 degrees) relative to the initial direction of sunlight (antisolar line) then you will notice that the sky is more intense than it is in other directions. As discussed before, the intensity is along a circular arc and is the rainbow you would see.  

Rainbow Formation with White Light

White light consists of a range of colours (see slide 9) - these are separated in the process of refraction because each colour has a different refractive index and bends differently from other colours (see slides 9 and 10).  Each colour ray behaves as monochromatic light and produces its own rainbow.  Slide 15 shows the case for red and violet rays while slide 16 shows the full spectrum. 
Slide 15:

Slide 16:

The colourful light produced by raindrops is received by the eye to perceive the arc of the rainbow.  We notice from slide 16 that in the spectrum red colour rays are deviated the least and should appear at the bottom of the rainbow.  But slide 3 shows that red arc is at the top of the primary rainbow. How?
Why is Red Colour at the Top of the Primary Rainbow?

When we observe a rainbow, our eye is at a fixed position in space and rays of light, whatever colour, must enter our eye for us to perceive them. Slides 17 and 18 show how light rays from different raindrops reach us.

Slide 17:

Slide 18:

Each drop sends a unique colour ray to the eye.  Because violet is deviated more than the red, raindrops generating violet colour are lower in sky than those producing red (see slides 17 and18).  The linear distance of the drops from the eye does not matter, only the angle determines what colour will reach us. That is why we see the colouful arcs of the rainbow with red arc positioned at the top.
Interestingly, raindrops are falling towards the Earth and continuously being replaced by others.  The rainbow we see is generated by new set of raindrops continuously replacing the previous set - it is really unique to the observer and ever-changing.

Why is the Sky Brighter under the Rainbow?
Why is there a Dark Region Between the Rainbows?

Slides 7, 17 and 18 provide a ready explanation why the sky is brighter under the rainbow.
Slide 19:

This is because primary rainbow is formed by one internal reflection of light in raindrops. Slide 7 demonstrated that the rainbow ray is the least deflected ray and raindrops generating these lie at about 42 degrees to the antisolar light. All other rays lie above the rainbow ray and to reach the eye, raindrops must be at a lower elevation than the rainbow arc. This internally reflected light makes the sky under the rainbow arc look brighter.  Slide 7 also shows that the angles that the various rays are travelling cover a wide angular range - this means that light rays of different colours overlap each other and the colour definition is washed out making the sky appear white.
Also little or no light is sent to the eye by raindrops above the primary rainbow arc and the region above the rainbow appears darker (Alexander's dark region). 

The Secondary Rainbow

Primary rainbows are formed by light internally reflecting once inside raindrops.  If the light reflects two times inside a raindrop then the dispersion in constituent colours still happens and the angle of deviation is different.  The rainbow is seen at an elevation of 51 degrees from the antisolar line.  Slide 20 is from hyper-physics website and demonstrates the formation of the secondary rainbow. 
Slide 20:

In secondary rainbows the order of colours is reversed with violet colour at the top of the rainbow.  The secondary rainbow is fainter - only about 10% as intense as the primary -  because it is more spread out and also at each reflection and refraction point, some light intensity is lost.

Rainbows and Water Drop Size

A bow's appearance depends on the size of the raindrops. Raindrops ~ 1 mm diameter produce bright narrow rainbows.  Smaller drops produce duller, broader rainbows.      Raindrops are never exactly identical in size.  Drops greater than 5 mm diameter are not common - as collisions between drops break them up. Surface of bigger drops also oscillates and degrades the sharpness of any rainbows produced by them.
The rainbow description had assumed that drops were spherical; which is certainly correct for drops up to about 0.3 mm diameter.  Larger drops tend to have flattened shapes due to air drag as they fall under earth's gravity. Flattened drops affect the distribution of the brightness in the rainbow arc.
For very small drops, 0.05 mm diameter, different colours start overlapping and the appearance of the rainbow takes a whitish hue.  This happens in fogs and clouds where the rainbows are practically white in colour.  Slide 21 shows a couple of examples of fogbows.
Slide 21:

Higher Order Rainbows

A detailed description of higher order rainbows is given in the August 2016 Review by Professor Haussmann.  We know that the primary (1st order) and secondary (2nd order) rainbows are produced by one and two internal reflections inside raindrops.  There is no reason that three or more internal reflections should not happen and produce the corresponding order rainbows. 

For red light, the calculated minimum deviation of incident rays (the rainbow ray) is as follows (angles in degrees)

Rainbow        Minimum       Rainbow          rainbow

  order            Deviation       Elevation         Angular 

                                                                        Size  

    1                  137.8               42.2                 0.9

    2                  129.3               50.7                 1.7

    3                    41.9             138.1                 2.4

    4                    43.4             136.6                 3.1

    5                  127.9               52.1                 3.7

    6                  148.1               31.9                 4.4

Rainbow Elevation is the direction with respect to the antisolar line that the rainbow should be visible.  We can notice the difficulty in viewing 3rd and 4th order rainbows. They are located in in the backward direction - direction facing the sun, they are also wider and less intense than the 1st and 2nd order rainbows.  5th order rainbow lies just below the 2nd order and is in the Alexander's band (the dark region between the 1st and 2nd order).  This makes the observation of higher order (3 and above) rainbows extremely difficult.
Slide 22:

Recently, however, 3rd and 4th order rainbows have been photographed. I show the only example that I can find in published literature:

Slide 23:

I refer you to Professor Haussmann's review for a detailed discussion of the observation of even higher order rainbows.

Moonbows

If the Moon is bright and similar conditions to normal rainbow formation are present - looking at rain clouds with the Moon shining behind you, then a bow may be observed.  In rare cases, the refracted light in raindrops may be intense enough to make the moonbow visible.
Because moonlight is much weaker than sunlight, a moonbow is not observed very often and the separation of colours is not clearly defined - the moonbow appears whitish. 
On 16th October 2016, we were lucky to have the super-moon light the skies with just the right conditions for observing a bow.  The Moon was bright and even the colours of the spectrum may be inferred in the moonbow.  I have used the following pictures of moonbows from the BBC website - they are truly remarkable photographs.

September 2020: For some beautiful pictures of Moonbows and Aurora together, Click here.

Final Word: Rainbows have been objects of awe and fascination since historic times.  Their vast size and majestic appearance has given rise to many myths and legends.  
How rainbows are produced may be explained at various levels of sophistication - I have provided the simplest description using ray optics.  Wave optics is required to explain the appearance of some dark bands at the edge of a rainbow  - I have considered this to be outside the scope of the present blog. A detailed mathematical description of rainbows may be found in a review (~140 pages) by Adams.
Other good source for rainbows is the Hyperphysics web site.

A nice detailed very readable article on rainbows (with emphasis on why Hawaii has the best rainbows? may be reached here)

I am grateful to Professor Haussmann for some very useful communications about this wonderful subject.

Hope you have enjoyed reading this blog about rainbows.  I would be happy to discuss/explain any questions about this topic.

Parallax - Measuring Distances to Stars; Visual Depth Perception, View from Moving Trains; Locating Virtual Images

  
Parallax is the apparent change in position of an object relative to distant background objects resulting from a change in position of the observer.
Parallax means change and is derived from the Greek word parallaxis.

When traveling in a fast moving train, children often ask questions about the rotating landscape ; the video link demonstrates very well this example of parallax.  

Schematically, the slide (adapted from Wiki) explains how parallax works: 

You can observe parallax if you first view the thumb of your stretched out hand against the objects near the wall with one eye closed. Now viewing the thumb with the other eye will show a shift in its previous position against the background objects. Do try this simple demonstration yourself. 
The two eyes see the thumb in different positions - actually our brain corrects for this change in apparent position as seen by the two eyes to provide one sharp image of the thumb. From this information (parallax), the brain also estimates the distance of the object from us - kind of 3-D perception already built in the processing of images we see with our eyes.  Many birds and insects, do not have much overlap in the fields of view for the two eyes and tend to move their head sideways or up and down to generate depth perception.  (This is called motion-parallax).

We now understand what parallax is - and that it is already useful for depth perception for humans.  What else is it good for?  As it turns out parallax is of fundamental importance in many fields.  I shall look at two in detail here - measuring distances to stars and locating virtual images.

Distances to Stars:  The first step in understanding the Universe is to measure its size - how far stars and galaxies are from the Earth.  Such distances are measured through a series of methods that have overlapping validity - a cosmic distance ladder.  Parallax method is the base rung of the ladder and other methods are calibrated using parallax measured distances as standard.
The distances involved are very large and require a large base line - biggest possible separation between the two points of observation.  The change in viewing direction - parallax angles - also get smaller as the distance to a star increases.  The biggest distance available to us is the diameter of Earth's orbit around the Sun - roughly 300 million kilometers.  The average value of the radius of Earth's orbit is very nearly 150 million km and is called the Astronomical Unit (AU). The following slides explain how distances to stars are determined by the parallax method:

The parallax method defines Parallax Second (parsec or pc) as a new unit of distance in astronomy. 

 "A star with a parallax of 1 arcsec has a distance of 1 parsec (pc). 

One parsec (pc) = 206,265 AU = 3.086 x10¹³ km.

Another unit of distance that is frequently used in astronomy is a Light Year (Ly).  Light travels 300 million km in one second.  

The distance travelled by light in a year is one light year. 

A light year (Ly) = 0.31 pc = 61,270 AU = 0.96 x 10¹³ km.  

For completeness:  1 pc = 3.26 Ly

From the slide, we notice that the distance D in pc to a star is equal to 1 AU divided by the parallax p in arcsec.

The parallax angles are generally very small and difficult to measure.  Temperature fluctuations in the atmosphere blur the star view and limit measurements to 0.01 arcsec or 100 pc - no more than 100 stars are in that range. 
Space based telescope Hipparcos (launched by ESA in 1989) provides a better more accurate measurement of star parallaxes down to 0.001 arcsec or distances to 1000 pc. Hipparcos has measured distances of about 100,000 stars. 1000 pc is still only a small fraction of the Milky way that is 30,000 pc across.
ESA launched Gaia in December 2013 to chart a 3-D map of the Milky Way to reveal the composition, formation and evolution of our Galaxy.  Gaia is designed to measure positions of more than 200 million stars to an accuracy of 0.00001 arcsec (distances to 100,000 pc).
On 13 September 2016, Gaia published the precise position and brightness of 1142 million stars.

Locating Virtual Images:  In a somewhat less esoteric application, parallax may be used to locate virtual images formed by mirrors and concave lenses.  Consider the case of a plane mirror - you see your image formed but where is it? How do you pin it down?  We can do it by using parallax.
The slide shows how a virtual image is formed in a plane mirror:  But where is it?

  

In the formation of the virtual image, rays of light from each point do not actually penetrate the mirror.  They are reflected back to you and appear to come from a point behind the mirror.  Geometrically, using the laws of reflection, it can be shown that the image is exactly the same distance behind the mirror as you are in front of it.  But can we locate it?

We can locate the virtual image using parallax method.  the idea is as follows:

If you view the two pins in the following slide along the line of sight shown, then they will appear to overlap.  But on moving the head sideways, they separate in a particular manner that helps you to decide which of the two pins is nearer to you.  

Well, this is essentially what you need to do.  Place a pin at the back of a plane mirror and change its position until the parallax between the pin and the virtual image is removed - they move together as one unit as you move your head sideways.  The position of the pin is the position of the virtual image.
Convex mirrors and concave lenses also form virtual images. These can be located following the same method that I have described for a plane mirror.

Human DNA Radiation Tolerance is Increased by the Unique Protein in Water Bears (Tardigrade)

In my 2010 lecture on the search for extraterrestrial life, I had discussed how some animals are known to survive extreme conditions of heat, radiation, pressure, vacuum etc. This is important because tolerance of such extreme conditions would indicate that life might have evolved even on planets which are on the periphery of the habitable zones. I reproduce a few slides from my lecture in the following:
  



It is clear that these species have evolved to withstand some of the most inhospitable environments imaginable. 

Tardigrade or Water Bears or moss piglets are one of the hardiest of animals.  They are tiny (0.05 to 1.2 mm long) and live near water. In adverse conditions of extreme hot or cold, very high pressures, space vacuum or intense UV/X-ray radiation water bears shrink, dehydrate and put metabolic activity on hold.  Dehydrated water bears can survive for years but come back to life when in contact with water which they need to grow and reproduce. 

The question is - how do they manage to survive the extreme conditions?  Such unusual tolerance of tardigrades has long fascinated researchers; however, the molecular mechanisms enabling such exceptional tolerance have remained largely unknown.  Water Bears Video
A study of tardigrade genome, published in Nature Communications this week has provided some amazing insight into the tolerance of tardigrade to extreme conditions.
I am reproducing their conclusions in the following slide.  (Apologies for the somewhat formal language of the slide but I feel it presents the researchers' conclusions in a pristine way)

What I find the most exciting is the demonstration that the unique proteins can also protect human cells against X-rays induced DNA damage and improve human tolerance to radiation.  This is a game-changer and as the authors say, there could be a bountiful source of protection genes and mechanisms.  

An interesting question to ask is how did R. varieornatus tardigrade acquire the genes for the unique protein - Hashimoto et al. call the protein Dsup (damage suppressor). 
This has been a controversial issue with some previous work suggesting that tardigrade acquired many of their genes from bacteria through a process called horizontal gene transfer (HGT) - an important mechanism for the evolution of many organisms.  This study - which is by far the most extensive and is a full genome sequence of a tardigrade - sets an upper limit of 1.2% on the contamination by foreign genes and claim that the protein Dsup is uniquely developed by the tardigrade itself.  
It was also demonstrated that Dsup protein affords DNA protection without impairing cell viability and is suitable for application to confer tolerance to other animal cells. 
In fact, Dsup-expressing human cultured cells exhibited better tolerance to 4 Gy of X-ray radiation. (One gray or Gy is the absorption of one joule of energy, in the form of ionizing radiation, per kilogram of matter). 

Will Future Water Crises Destroy Our Civilization? - Probably Not - But Only if We Start Paying Attention Now...

(Click on a slide to see its full page image; press ESC to return to text)

Freshwater is one of the four pillars on which our civilization rests - the others are food, energy and the climate. Humans have adversely impacted all - in a big way - no wonder the new epoch is called the anthropocene. How long will it last? - Humans will have the control on that too!

I had looked at food in a recent blog. Water is fundamental to our survival - water is a marvel of nature with such unique properties that without these the very existence of life would not be possible.  I recommend highly that you look at the Wiki article to feel amazed how this simple molecule can express myriad of such wonderful properties.

To put the subject in context, I shall take a brief historical look before discussing the present situation.  Then, I shall detail a few ideas about tackling the water crisis to ensure adequate freshwater supply to all of the world population in 50 years time. 

Historical Context:  Climate change and water in particular have been linked to the demise of many of the great ancient civilizations.  The first of the following two slides provides a summary and the second slide tells a case history of the Indus Valley Civilization (IVC) to demonstrate that these were advanced societies with well thought out and established system of civil engineering, governance etc.

IVC lasted over 6000 years - much longer than the present western civilization.  I am sure the quality of life was also very reasonable - and they say that people lived peacefully with no wars. 
We note that the populations in these ancient civilizations were relatively small - a few million people - and they always developed in areas where water supply would be plentiful. However, they did not have the means to shift a lot of people over vast distances to escape from natural climate changes and resulting water shortages.

Current Situation: In our technologically advanced societies, we understand the global conditions very well and have good scientific understanding of the Earth's hydrological cycle.   

The amount of water in the world is fixed; freshwater is a mere 2.5% of the total.  To make matters more difficult, accessible freshwater is only 0.008% of all water. (see slide).

Of the 0.008% global freshwater, we use almost 90% in industrial and agricultural activity. Domestic use accounts for a mere 10% of this freshwater.  Growing population with improving living standards will create extra food demand - higher agricultural output will be needed with corresponding call for extra water resources - the current situation looks hopelessly unsustainable.  

To understand the magnitude of the problem facing the world, we need to look at the way water is used in agriculture to produce food. 

Naturally, large populations settled in area that had big promise of rain-fed irrigation - water was plentiful to grow food.  Then, we also learnt that irrigation is helped by drawing water from rivers and aquifers (groundwater or fossil water).  Even today, 80% of the agriculture production is by rain-fed water.  The three main users of freshwater - agriculture, industries and domestics - share the global freshwater supply.   70% of global freshwater is used for irrigation that produces the remaining 20% of the food. This is the biggest call on global freshwater supply and there lies the problem.

Global warming (GW) is an established fact - our Earth is heating - both land and seas. This has many consequences that are well researched and reported.  For our context, the main point is that warming of the seas increases evaporation and also disturbs the exchange of energy between the oceans and the air in the atmosphere (remember that water in the oceans absorbs the greatest part of the solar energy that falls on the Earth and this energy is then redistributed through global air and water circulation patterns).  Air circulation carries moist air to various parts of the globe and causes rainfall - that is responsible for 80% of food production in the world. GW is predicted to affect the way air circulates with consequences in terms of shifting rain fall patterns.  Areas that currently receive large amounts of water may experience droughts; but that is where the populations are and agricultural land produces most of the food.  The result will be loss of agricultural yields, famines and mass migration.

A second threat is our dependence on groundwater for irrigation and domestic use.  Groundwater is water that is trapped underground in aquifers.  Some aquifers are closed and are not replenished by rainwater while others do get topped up by rain.  If the withdrawal rate of water from aquifers is greater than replenish rate then total amount of water available will be reduced and is indicated by the increasing depth that pipes must be dug to reach the water levels. The following slide indicates the regions of current water stress:

The situation is even more serious for aquifers that are closed (not recharged by rain) as in the Middle East.  An interesting case study is of Saudi Arabia who once sat on a large body of water in an ancient aquifer.  Around 1970, Saudi regime decided to become self sufficient in food by using water from their aquifer.  The slide tells what happened... 

Climate change will affect many areas by either making them too hot to live and/or by creating drought conditions.  This will result in mass migration of populations creating many social, political and financial problems.  Resettling of refugees will also require additional strains on the food and water resources.
The above discussion emphasizes the need to be careful how we plan our policies and actions. Future is uncertain and climate change effects must also be taken into account in forming policies. Some common sense steps pop up:

Currently, agriculture uses 70% of the available freshwater.  If we can reduce the water usage in agriculture by 20% then domestic water availability will more than double from 10% to 24%. This alone would be enough to supply potable water for 10 billion people.  Good agricultural practices like drip irrigation can achieve this but are still not widely used.

Water from aquifers should only be withdrawn at rates that does not reduce the total volumes available - rate of withdrawal must not exceed recharge rate.  This will impact on irrigation but must be taken into account as a prudent step.
Coastal areas have desalinated seawater to provide freshwater - desalination is a energy intensive process - and the use of fossil fuels for desalination contributes to global warming.  Better technology here will help.
Water is a precious commodity and recycling of waste water is a must.  Good progress has been made in the past decades in recycling technologies.
  
Addressing water scarcity issues:   I float a few ideas in the following - with particular emphasis on water desalination processes:
a. Agriculture uses 70% of freshwater:  How does one reduce the consumption of water used in agriculture?  In my previous blog, I had addressed the question of sustainable food supplies.  Switching our diet from animal protein to plant protein will be enormously effective and will eliminate the need to expand arable land, at the same time reducing the water requirements. I had discussed hydroponic farming that uses water (and land) extremely efficiently.  3-D printing of food holds a big promise in terms of reducing waste in food production.  Reducing loss of food in storage, transportation and in homes can save up to 15%.  

In traditional agriculture, drip-irrigation can save up to 50% water requirements.  Drip irrigation has a serendipitous discovery that is worth recounting here:
In the 1930s, a water engineer was visiting his friend in a desert in Israel when he noticed a line of trees with one member that was much taller and more robust looking than the others. He did a little digging, literally, and found that a household water line running along the tree line had sprung a leak in the area of that one tree and was feeding it with a steady drip drip drip of water.  The wet area spot on the surface didn't seem like much, but down below was a large onion-shaped area of juicy soil.

b. Drinking Water:  While there is much scope of reducing the use of freshwater in agriculture - this can not be the whole solution. Many of the world's coastal areas suffer from lack of drinking water. Sea water contains about 3.5% salt and is not good for human consumption or for agricultural use. Some areas, as in the Middle East, also experience drought conditions regularly. Many urban areas, particularly in developing countries, have poor water supply systems. Currently, more than 1 billion people do not have supply of safe drinking water. The mantra for supplying potable water has to be to minimize waste, collect and recycle all available water.
Rainwater Harvesting has been practiced in semi-arid areas for centuries but has become much more common recently.  Some countries require new homes to have adequate rain collection systems.  Rainwater is essentially pure water and is suitable for drinking.  Rainwater collected in tanks is still quite clean and is suitable for general household purpose and also for irrigation.  Rainwater harvesting is an excellent example of harnessing a resource that is essentially cost free, is widely available and is already helping in mitigating water scarcity in semi-arid areas around the world.

Recycling:  Recycling water makes sense.  An extreme example of recycling water is at the International Space Station (ISS) where 93% of all water is recycled.  Treated wastewater from residential buildings and industries can be reused for many useful tasks such as agriculture and landscape irrigation, industrial processes, toilet flushing and also recharging groundwater aquifers. Recycled water can satisfy most water demands, so long as it is adequately treated to ensure water quality appropriate for the use.

Water Desalination    has long been used in water-scarce regions to increase drinking water availability.  Currently, 11 billion gallons desalinated water is produced globally everyday.  Water desalination (WD) not only holds great promise for solving future water scarcity problems but also it is being used for desalting brackish (moderately saline) water and for softening and removal of organics and impurities in groundwater. Unfortunately, the quality of conventional freshwater sources is being degraded by pollution etc and a process to improve general water quality is required. Membrane separation is a cost-effective way to achieve this.

In the words of John F Kennedy:  If we could ever competitively, at a cheap rate, get freshwater from seawater...(this) would be in the long-term interests of humanity which could really dwarf any other scientific accomplishment.

WD can be performed either by thermal distillation or by membrane separation. The following two slides are adapted from Banat.

Thermal Distillation:  Over 60% of the world's desalted ocean water is produced by boiling seawater to produce water vapour that is then condensed to form freshwater. 

Thermal distillation plants produce water with salt concentrations from 5 to 50 parts per million - seawater salt content is 35000 ppm.  Thermal distillation is highly energy intensive and so far the energy source has been fossil fuels which is damaging for the environment and the climate.  Middle East with about 50% of the global desalination capacity has plenty of cheap oil and there has been little incentive to use renewable energy sources.  In fact, it is the drought affected areas that need to desalinate water and these are the areas where solar energy is plentiful.  With prices of solar cells plummeting, it is expected that solar renewable energy will replace fossil fuel for thermal distillation.  Currently the energy cost is about 13 kWh or one US dollar per cubic meter of thermally desalinated water.   

Membrane Separation Processes (MSP):  

Nano-filtration (NF); Reverse Osmosis (RO)

Membrane separation processes (MSP) use a membrane - a filter or a semi-permeable membrane - to produce drinking water in a more cost-effective manner than thermal distillation.  Water can have impurities that are either suspended (microbes, chemicals, dirt etc.) or dissolved (salt, minerals etc.). These are detailed in the following slide

For desalination where sea salt (NaCl) is dissolved in water at a concentration of 3.5% and is in ionized state, the process used is reverse osmosis (RO).  RO was developed in the 1960s and represents a serious breakthrough in desalination technologies. Let me explain this in more detail:

In osmosis, two solutions with different salt concentrations and separated by a semi-permeable (also called partially or selectively permeable) membrane (SMP) have a tendency to make the concentration equal in both parts.  This is achieved by the solute molecules (water in our case) passing through the SMP from lower concentration side to higher concentration side.  SMP does not allow impurity molecules (salt ions in our case) to pass through - only water molecules can. 

In reverse osmosis a change in the direction that salt water naturally seeks is achieved; and water molecules from high concentration (seawater side) move through the membrane to the low concentration side (pure water). This is done by applying high pressure on the seawater side of the system.

In fact, the RO water is so pure  - de-ionised or de-mineralized - that it is mixed with some original salt water to be suitable for drinking.

RO systems are good to desalinate all types of water and also for the removal of contaminants like radio-nuclides, nitrates, arsenic, pesticides etc.  Nano-filteration (NF) uses lower pressures and is useful for the treatment of hard,  coloured water, viruses, and also high organic content feedwater.  
The cost of RO desalination is about half of the cost of thermal desalination; energy costs are 30% and membrane replacement costs (a typical lifetime of the membrane is 5 years) 10%.  These costs have been coming down - membranes are 5 times cheaper since 1970.  In traditional water-short areas the costs of desalted water are already competitive with conventional water sources.

It is hoped that with renewable energy becoming more widely available with improved affordability, water desalination will not only supply sufficient potable water to water-scarce coastal areas but also we shall be able to use brackish (less salted) water, wastewater etc.  This will increase the available water pool size.  Additionally, recycling of water with membrane technology holds the promise of satisfying domestic residential water requirements.

New technologies are coming up that could make filtration much cheaper and efficient.  See

Final Word:  I have considered the ways in which sufficient potable water can be made available to 10 billion people in about 50 years time.  The technology is there already and in the future, systems will become more efficient with even lower costs. Irrigated agriculture water supply situation requires more widely adopting methods like drip-feeding, hydroponic farming that are well tested but requires better information to be made available to farmers.  Switching from animal protein to plant protein will solve the water problem in a big way but this requires a change of culture and habits - these tend to be difficult asks - but one hopes that with good official backing (UN is already promoting the shift) from individual governments, people may be convinced over the next decades to consume more plant proteins.
But then one also has to ask the question  - that with plentiful food and water available, why in the world today over one billion people do not have enough to eat and sufficient potable water to drink?
My biggest concern remains climate change.  Shifting rainfall patterns can cause havoc for indigenous populations and forced mass migration from such areas can destabilize our already fragile geo-political order. Is it too late to do something substantial to mitigate the effects of climate change?