Angle of incidence
Angle of incidence is a measure of deviation of something from "straight on", for example:
  • in the approach of a ray
    Ray (optics)
    In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

     to a surface, or
  • the angle at which the wing
    A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

     or horizontal tail
    Stabilizer (aircraft)
    In aviation, a stabilizer provides stability when the aircraft is flying straight, and the airfoil of the horizontal stabilizer balances the forces acting on the aircraft....

     of an airplane is installed on the fuselage
    The fuselage is an aircraft's main body section that holds crew and passengers or cargo. In single-engine aircraft it will usually contain an engine, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage which in turn is used as a floating hull...

    , measured relative to the axis of the fuselage.


In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

. The ray can be formed by any wave: optical, acoustic, microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

, X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

 and so on. In the figure above, the red line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the critical angle
Critical angle
Critical angle can refer to:*Critical angle the angle of incidence above which total internal reflection occurs*Critical angle of attack, in aerodynamics; the angle of attack which produces the maximum lift coefficient...

. The angle of reflection and angle of refraction are other angles related to beams.

Grazing angle

When dealing with a beam that is nearly parallel to a surface, it is sometimes more useful to refer to the angle between the beam and the surface, rather than that between the beam and the surface normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

, in other words 90° minus the angle of incidence. This angle is called a glancing angle or grazing angle. Incidence at small grazing angle is called "grazing incidence".

Grazing incidence diffraction
Grazing incidence diffraction
Grazing incidence X-ray and neutron diffraction , typically from a crystalline structure uses small incident angles for the incoming X-ray or neutron beam, so that diffraction can be made surface sensitive. It is used to study surfaces and layers because wave penetration is limited. Distances are...

 is used in X-ray spectroscopy
X-ray spectroscopy
X-ray spectroscopy is a gathering name for several spectroscopic techniques for characterization of materials by using x-ray excitation.-Characteristic X-ray Spectroscopy:...

 and atom optics
Atom optics
Atom optics is the area of physics which deals with beams of cold, slowly moving neutral atoms, as a special case of a particle beam....

, where significant reflection can be achieved only at small values of the grazing angle. Ridged mirror
Ridged mirror
In atomic physics, a ridged mirror is a kind of atomic mirror, designed for the specular reflection of neutral particles coming at the grazing incidence angle, characterised in the following: in order to reduce the mean attraction of particles to the surface and increase the reflectivity, this...

s are designed for reflection of atoms coming at small grazing angle. This angle is usually measured in milliradians.

Determining the grazing angle with respect to a planar surface is trivial, but the computation for almost any other surface is significantly more difficult. The exact solution for a sphere (which has important applications in astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

 and computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....

) was an open problem for nearly 50 years until a closed-form result was derived by mathematicians Allen R Miller
Allen R Miller
Allen R Miller was an American mathematician.Miller was a major contributor to the field of special functions, especially confluent hypergeometric functions.-Biography:...

 and Emanuel Vegh in 1991.

Angle of incidence of fixed-wing aircraft

On fixed-wing aircraft
Fixed-wing aircraft
A fixed-wing aircraft is an aircraft capable of flight using wings that generate lift due to the vehicle's forward airspeed. Fixed-wing aircraft are distinct from rotary-wing aircraft in which wings rotate about a fixed mast and ornithopters in which lift is generated by flapping wings.A powered...

, angle of incidence is the angle between the chord line
Chord (aircraft)
In aeronautics, chord refers to the imaginary straight line joining the trailing edge and the center of curvature of the leading edge of the cross-section of an airfoil...

 of the wing where the wing is mounted to the fuselage and the longitudinal axis of the fuselage. The angle of incidence is fixed in the design of the aircraft by the mounting of the wing to the fuselage.
The term can also be applied to horizontal surfaces in general (such as canards or horizontal stabilizers) for the angle they make relative the longitudinal axis of the fuselage.

The figure to the right shows a side view of an airplane. The extended chord line of the wing root (red line) makes an angle with the longitudinal axis (roll axis) of the aircraft (blue line). Wings are typically mounted at a small positive angle of incidence, to allow the fuselage to be "flat" to the airflow in normal cruising flight. Angles of incidence of about 6° are common on most general aviation
General aviation
General aviation is one of the two categories of civil aviation. It refers to all flights other than military and scheduled airline and regular cargo flights, both private and commercial. General aviation flights range from gliders and powered parachutes to large, non-scheduled cargo jet flights...


Other terms for angle of incidence in this context are rigging angle and rigger's angle of incidence. It should not be confused with the angle of attack
Angle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...

, which is the angle the wing chord presents to the airflow in flight. Note that some ambiguity
Ambiguity of words or phrases is the ability to express more than one interpretation. It is distinct from vagueness, which is a statement about the lack of precision contained or available in the information.Context may play a role in resolving ambiguity...

 in this terminology exists, as some engineering texts that focus solely on the study of airfoils and their medium may use either term when referring to angle of attack. The use of the term "angle of incidence" to refer to the angle of attack occurs chiefly in British usage.

See also

  • Effect of sun angle on climate
    Effect of sun angle on climate
    The amount of heat energy received at any location on the globe is a direct effect of sun angle on climate, as the angle at which sunlight strikes the Earth varies by location, time of day, and season due to the Earth's orbit around the sun and the Earth's rotation around its tilted axis...

  • Reflection (physics)
    Reflection (physics)
    Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

  • Refraction
    Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

  • Season
    A season is a division of the year, marked by changes in weather, ecology, and hours of daylight.Seasons result from the yearly revolution of the Earth around the Sun and the tilt of the Earth's axis relative to the plane of revolution...

  • Snell's law
    Snell's law
    In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

  • Total internal reflection
    Total internal reflection
    Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...

External links

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