# Minimum Angle of Deviation

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**This is one of a set of almost 40 diagrams exploring Rainbows.**

**Each diagram appears on a separate page and is supported by a full explanation.**

- Follow the links embedded in the text for definitions of all the key terms.
- For quick reference don’t miss the summaries of key terms further down each page.

## Description

#### Minimum Angle of Deviation

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#### About the diagram

###### About the minimum angle of deviation

The *minimum angle of deviation* of a ray of light of any specific wavelength passing through a raindrop is the smallest angle to which it must change course before it becomes visible within the arcs of a rainbow to an observer.

- Any ray of light (stream of photons) travelling through empty space, unaffected by gravitational forces, travels in a straight line forever.
- When light travels from a vacuum or from one transparent medium into another, it deviates from its original path (and changes speed).
- The more a ray changes direction the greater its angle of deviation.
- A ray reflected directly back on itself has an angle of deviation of 180
^{0}– the maximum possible angle of deviation. - It is the optical properties of air and raindrops that determines the angle of deviation of any ray of incident light.
- It is the optical properties of raindrops that prevent any ray of visible light within the visible spectrum from exiting a raindrop towards an observer at an angle of deviation less than 137.6
^{0}. - The angle of deviation and the
*angle of deflection*are directly related to one another and together always add up to 180^{0}. - The angle of deviation and the viewing angle are always the same.

###### More about the minimum angle of deviation

- The optical properties of an idealised spherical raindrop mean that no light of any particular wavelength can deviate at less than its minimum angle of deviation.
- The minimum angle of deviation of visible light depends on its wavelength.
- The
*minimum angle of deviation*for red light with a wavelength of approx. 720 nm is 137.6^{0}but similar rays of the same wavelength but with other impact parameters can deviate up to a maximum of 180^{0}. - Different colours have different minimum angles of deviation because the refractive index of water changes with wavelength.

###### Impact parameter and minimum angle of deviation

- To form a primary rainbow, incident light must strike each raindrop above its horizontal axis.
- Rays of incident light of a single wavelength strike a raindrop at every possible point on the side of a raindrop facing the Sun.
- Only those that strike above the horizontal axis contribute to a primary rainbow.
- Points of impact of incident light striking a droplet can be measured on an impact parameter scale.
- It is the point of impact of rays of incident light of the same wavelength that is the variable factor that determines their subsequently different paths.
- Rays that strike nearest the horizontal axis, so with a value near 0.0 on an impact parameter scale have the largest angles of deviation.
- Rays that strike farthest away from the horizontal axis (near the topmost point on an impact parameter scale and so near 1.0) also have a large angle of deviation.

#### Some key terms

The angle of incidence refers to the angle at which incoming light strikes a surface and is measured between a ray of incoming light and an imaginary line called the normal.

- In optics, the
*normal*is a line drawn on a ray diagram perpendicular to, so at a right angle to (90^{0}), the boundary between two media. - The angle at which incident light from the Sun or a light bulb strikes a surface can affect the outcome. For instance, when incident light hits a mirror, the angle of incidence determines the angle of reflection.

The angle of reflection measures the angle at which light rebounds from a surface after being reflected.

- The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the
*normal*. - In optics, the
*normal*is a line drawn on a ray diagram perpendicular to, so at a right angle to (90^{0}), the boundary between two media. - The angle of reflection can be used to understand how light will behave when it interacts with different types of surfaces and objects.

- When discussing the formation of rainbows, the angle of deflection measures the angle between the initial path of a light ray before it hits a raindrop, and the angle of deviation, which measures how much the ray bends back on itself in the course of refraction and reflection towards an observer.
- See this diagram for an explanation: Rainbow anatomy
- The angle of deflection and the angle of deviation are always directly related to one another and together add up to 180 degrees.
- The angle of deflection equals 180 degrees minus the angle of deviation. So, it’s clear the angle of deviation is always equal to 180 degrees minus the angle of deflection.
- In any particular case, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow all follow paths that run parallel with the rainbow axis.

The angle of reflection is the angle between the incident light ray and the reflected light ray, both measured from an imaginary line called the normal.

- According to the law of reflection, the angle of incidence (the angle between the incident ray and the normal) is always equal to the angle of reflection.
- The angle of reflection is measured between the reflected ray of light and an imaginary line perpendicular to the surface, known as the normal.
- In optics, the normal is a straight line drawn on a ray-tracing diagram at a 90º angle (perpendicular) to the boundary where two different media meet.
- Expressed more formally, in optics, the normal is a geometric construct, a line drawn perpendicular to the interface between two media at the point of contact. This conceptually defined reference line is crucial for characterizing various light-matter interactions, such as reflection, refraction, and absorption.
- If the boundary between two media is curved, the normal is drawn perpendicular to the tangent to that point on the boundary.
- Reflection can be diffuse (when light reflects off rough surfaces) or specular (in the case of smooth, shiny surfaces), affecting the direction of reflected rays.

- The angle of reflection measures the angle at which reflected light bounces off a surface.
- The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the
*normal*. - See this diagram for an explanation: Reflection of a ray of light
- In optics, the
*normal*is a line drawn on a ray diagram perpendicular to, so at a right angle to (90^{0}), the boundary between two media. - If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

The angle of refraction measures the angle to which light bends as it crosses the boundary between different media.

- The angle of refraction is measured between the bent ray and an imaginary line called the
*normal*. - In optics, the
*normal*is a line drawn on a ray diagram perpendicular to, so at a right angle to (90^{0}), the boundary between two media. - Snell’s law is a formula used to describe the relationship between the angle of incidence and the angle of refraction when light crosses the boundary between transparent media, such as water and air or water and glass.

The angle of incidence measures the angle at which incoming light strikes a surface.

- When light is travelling towards something it is said to be incident to that surface or object.
- The angle of incidence is measured between a ray of incoming light and an imaginary line called the
*normal*. - In optics, the
*normal*is a line drawn on a ray diagram perpendicular to, so at a right angle to (90^{0}), the boundary between two media. - Expressed more formally, in optics, the normal is a geometric construct, a line drawn perpendicular to the interface between two media at the point of contact. This conceptually defined reference line is crucial for characterizing various light-matter interactions, such as reflection, refraction, and absorption.
- Incident light may have travelled from the Sun or a man-made source or may have already been reflected off another surface such as a mirror.
- When incident light strikes a surface or object it may undergo absorption, reflection, refraction, transmission or any combination of these optical effects.

- The angle of incidence measures the angle at which incoming light strikes a surface.
- The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.
- See this diagram for an explanation: Reflection of a ray of light
- In optics, the
*normal*is a line drawn on a ray diagram perpendicular to, so at a right angle to (90^{0}), the boundary between two media. - If the boundary between the media is curved, then the normal is drawn at a tangent to the boundary.