Radar
Watson-Watt was sent to the U.S. in 1941 to advise on air defense after Japan's attack on Pearl Harbor. Alfred Lee Loomis organized the secret MIT Radiation Laboratory at Massachusetts Institute of Technology, Cambridge, Massachusetts which developed microwave radar technology in the years 1941–45. Later, in 1943, Page greatly improved radar with the monopulse technique that was used for many years in most radar applications.
The war precipitated research to find better resolution, more portability, and more features for radar, including small, lightweight sets to equip night fighters (aircraft interception radar) and maritime patrol aircraft (air-to-surface-vessel radar), and complementary navigation systems like Oboe used by the RAF's Pathfinder.

Applications: The information provided by radar includes the bearing and range (and therefore position) of the object from the radar scanner. It is thus used in many different fields where the need for such positioning is crucial. The first use of radar was for military purposes: to locate air, ground and sea targets. This evolved in the civilian field into applications for aircraft, ships, and automobiles.
In aviation, aircraft can be equipped with radar devices that warn of aircraft or other obstacles in or approaching their path, display weather information, and give accurate altitude readings. The first commercial device fitted to aircraft was a 1938 Bell Lab unit on some United Air Lines aircraft. Aircraft can land in fog at airports equipped with radar-assisted ground-controlled approach systems in which the plane's position is observed on precision approach radar screens by operators who thereby give radio landing instructions to the pilot, maintaining the aircraft on a defined approach path to the runway. Military fighter aircraft are usually fitted with air-to-air targeting radars, to detect and target enemy aircraft. In addition, larger specialized military aircraft carry powerful airborne radars to observe air traffic over a wide region and direct fighter aircraft towards targets.
Marine radars are used to measure the bearing and distance of ships to prevent collision with other ships, to navigate, and to fix their position at sea when within range of shore or other fixed references such as islands, buoys, and lightships. In port or in harbour, vessel traffic service radar systems are used to monitor and regulate ship movements in busy waters.
Meteorologists use radar to monitor precipitation and wind. It has become the primary tool for short-term weather forecasting and watching for severe weather such as thunderstorms, tornadoes, winter storms, precipitation types, etc. Geologists use specialized ground-penetrating radars to map the composition of Earth's crust. Police forces use radar guns to monitor vehicle speeds on the roads. Automotive radars are used for adaptive cruise control and emergency breaking on vehicles by ignoring stationary roadside objects that could cause incorrect brake application and instead measuring moving objects to prevent collision with other vehicles. As part of Intelligent Transport Systems, fixed-position stopped vehicle detection (SVD) radars are mounted on the roadside to detect stranded vehicles, obstructions and debris by inverting the automotive radar approach and ignoring moving objects. Smaller radar systems are used to detect human movement. Examples are breathing pattern detection for sleep monitoring and hand and finger gesture detection for computer interaction. Automatic door opening, light activation and intruder sensing are also common.

Principles: 

Radar signal: A radar system has a transmitter that emits radio waves known as radar signals in predetermined directions. When these signals contact an object they are usually reflected or scattered in many directions, although some of them will be absorbed and penetrate into the target. Radar signals are reflected especially well by materials of considerable electrical conductivity—such as most metals, seawater, and wet ground. This makes the use of radar altimeters possible in certain cases. The radar signals that are reflected back towards the radar receiver are the desirable ones that make radar detection work. If the object is moving either toward or away from the transmitter, there will be a slight change in the frequency of the radio waves due to the Doppler effect.
Radar receivers are usually, but not always, in the same location as the transmitter. The reflected radar signals captured by the receiving antenna are usually very weak. They can be strengthened by electronic amplifiers. More sophisticated methods of signal processing are also used in order to recover useful radar signals.
The weak absorption of radio waves by the medium through which they pass is what enables radar sets to detect objects at relatively long ranges—ranges at which other electromagnetic wavelengths, such as visible light, infrared light, and ultraviolet light, are too strongly attenuated. Weather phenomena, such as fog, clouds, rain, falling snow, and sleet, that block visible light are usually transparent to radio waves. Certain radio frequencies that are absorbed or scattered by water vapour, raindrops, or atmospheric gases (especially oxygen) are avoided when designing radars, except when their detection is intended.

Illumination: Radar relies on its own transmissions rather than light from the Sun or the Moon, or from electromagnetic waves emitted by the target objects themselves, such as infrared radiation (heat). This process of directing artificial radio waves towards objects is called illumination, although radio waves are invisible to the human eye as well as optical cameras.

Reflection: If electromagnetic waves travelling through one material meet another material, having a different dielectric constant or diamagnetic constant from the first,
the waves will reflect or scatter from the boundary between the materials. This means that a solid object in air or in a vacuum, or a significant change in atomic density between the object and what is surrounding it, will usually scatter radar (radio) waves from its surface. This is particularly true for electrically conductive materials such as metal and carbon fibre, making radar well-suited to the detection of aircraft and ships. Radar absorbing material, containing resistive and sometimes magnetic substances, is used on military vehicles to reduce radar reflection. This is the radio equivalent of painting something a dark colour so that it cannot be seen by the eye at night.
Radar waves scatter in a variety of ways depending on the size (wavelength) of the radio wave and the shape of the target. If the wavelength is much shorter than the target's size, the wave will bounce off in a way similar to the way light is reflected by a mirror. If the wavelength is much longer than the size of the target, the target may not be visible because of poor reflection. Low-frequency radar technology is dependent on resonances for detection, but not identification, of targets. This is described by Rayleigh scattering, an effect that creates Earth's blue sky and red sunsets. When the two length scales are comparable, there may be resonances. Early radars used very long wavelengths that were larger than the targets and thus received a vague signal, whereas many modern systems use shorter wavelengths (a few centimetres or less) that can image objects as small as a loaf of bread.
Short radio waves reflect from curves and corners in a way similar to glint from a rounded piece of glass. The most reflective targets for short wavelengths have 90° angles between the reflective surfaces. A corner reflector consists of three flat surfaces meeting like the inside corner of a cube. The structure will reflect waves entering its opening directly back to the source. They are commonly used as radar reflectors to make otherwise difficult-to-detect objects easier to detect. Corner reflectors on boats, for example, make them more detectable to avoid collision or during a rescue. For similar reasons, objects intended to avoid detection will not have inside corners or surfaces and edges perpendicular to likely detection directions, which leads to "odd" looking stealth aircraft. These precautions do not totally eliminate reflection because of diffraction, especially at longer wavelengths. Half wavelength long wires or strips of conducting material, such as chaff, are very reflective but do not direct the scattered energy back toward the source. The extent to which an object reflects or scatters radio waves is called its radar cross section.

Radar range equation: The power Pr returning to the receiving antenna is given by the equation:

  
    
      
        
          P
          
            r
          
        
        =
        
          
            
              
                P
                
                  t
                
              
              
                G
                
                  t
                
              
              
                A
                
                  r
                
              
              σ
              
                F
                
                  4
                
              
            
            
              
                
                  (
                  4
                  π
                  )
                
                
                  2
                
              
              
                R
                
                  t
                
                
                  2
                
              
              
                R
                
                  r
                
                
                  2
                
              
            
          
        
      
    
    {\displaystyle P_{r}={\frac {P_{t}G_{t}A_{r}\sigma F^{4}}{{(4\pi )}^{2}R_{t}^{2}R_{r}^{2}}}}
  

where

Pt = transmitter power
Gt = gain of the transmitting antenna
Ar = effective aperture (area) of the receiving antenna; this can also be expressed as 
  
    
      
        
          
            
              G
              
                r
              
            
            
              λ
              
                2
              
            
          
        
        
          4
          π
        
      
    
    {\displaystyle {G_{r}\lambda ^{2}} \over {4\pi }}
  
, where

  
    
      
        λ
      
    
    {\displaystyle \lambda }
  
 = transmitted wavelength
Gr = gain of receiving antenna
σ = radar cross section, or scattering coefficient, of the target
F = pattern propagation factor
Rt = distance from the transmitter to the target
Rr = distance from the target to the receiver.