# Reflection & Refraction in a Raindrop

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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.
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## Description

#### Reflection & Refraction in a Raindrop

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Yes! The angle of incidence of a ray of light as it strikes any point on a surface is always the same as the angle of reflection.
Yes! When light leaves a vacuum or travels from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.
Refraction refers to the way light changes speed and direction as it travels across the interface between one transparent medium to another.
Yes! As light crosses the boundary from a faster medium such as air to a slower medium such as glass or water it bends towards the normal.

###### Overview of raindrops

An idealized raindrop forms a sphere. These are the ones that are favoured when drawing diagrams of both raindrops and rainbows because they suggest that when light, air and water droplets interact they produce predictable and replicable outcomes.

• In real-life, full-size raindrops don’t form perfect spheres because they are composed of water which is fluid and held together solely by surface tension.
• In normal atmospheric conditions, the air a raindrop moves through is itself in constant motion, and, even at a cubic metre scale or smaller, is composed of areas at slightly different temperatures and pressure.
• As a result of turbulence, a raindrop is rarely in free-fall because it is buffeted by the air around it, accelerating or slowing as conditions change from moment to moment.
• The more spherical raindrops are, the better defined is the rainbow they produce because each droplet affects incoming sunlight in a consistent way. The result is stronger colours and more defined arcs.
###### Real-life raindrops
• Raindrops start to form high in the atmosphere around tiny particles called condensation nuclei — these can be composed of particles of dust and smoke or fragments of airborne salt left over when seawater evaporates.
• Raindrops form around condensation nuclei as water vapour cools producing clouds of microscopic droplets each of which is held together by surface tension and starts off roughly spherical.
• Surface tension is the tendency of liquids to shrink to the minimum surface area possible as their molecules cohere to one another.
• At water-air interfaces, the surface tension that holds water molecules together results from the fact that they are attracted to one another rather than to the nitrogen, oxygen, argon or carbon dioxide molecules also present in the atmosphere.
• As clouds of water droplets begin to form, they are between 0.0001 and 0.005 centimetres in diameter.
• As soon as droplets form they start to collide with one another. As larger droplets bump into other smaller droplets they increase in size — this is called coalescence.
• Once droplets are big and heavy enough they begin to fall and continue to grow. Droplets can be thought to be raindrops once they reach 0.5mm in diameter.
• Sometimes, gusts of wind (updraughts) force raindrops back into the clouds and coalescence starts over.
• As full-size raindrops fall they lose some of their roundness, the bottom flattens out because of wind resistance whilst the top remains rounded.
• Large raindrops are the least stable, so once a raindrop is over 4 millimetres it may break apart to form smaller more regularly shaped drops.
• In general terms, raindrops are different sizes for two primary reasons,  initial differences in particle (condensation nuclei) size and different rates of coalescence.
• As raindrops near the ground, the biggest are the ones that bump into and coalesce with the most neighbours.
###### The laws of reflection and refraction
• Primary rainbows form when incident light strikes raindrops above their horizontal axis reflecting once off the inside before exiting towards an observer.
• Incident light that strikes raindrops below their horizontal axis and reflects once on the inside before exiting, directs light upwards away from an observer.
• Secondary rainbows form when incident light strikes raindrops below their horizontal axis reflecting twice off the inside before exiting downwards.
• The Law of reflection deals with the angles of incidence and reflection when light strikes and bounces back off a surface and can be used for calculations relating to the curved surfaces of raindrops.
• Remember that the law of reflection states that the angle of incidence always equals the angle of reflection for a mirror-like (specular) surface.
• The Law of Refraction (Snell’s law) deals with the changes in the speed and direction of incident light as it crosses the boundaries between air and a raindrop and then between a raindrop and the surrounding air.
• The diagram shows an incident ray of white light striking a raindrop.
• The path of a red ray is traced through the raindrop as reflection and refraction cause it to be deflected back towards the observer.
• Only the path of a red ray is shown because light of other wavelengths is refracted at slightly different angles.
• At the point of impact of the incident ray, light crosses the boundary and is refracted towards the normal. Notice that a proportion of light reflects back off the surface.
• When the ray strikes the far side of the droplet, the ray is reflected back into the droplet, with the angle of incidence on the surface being the same as the angle of reflection. Notice that a proportion of light exits the droplet at this point.
• When the ray strikes the surface for the third time the ray undergoes refraction again as it crosses the boundary. A proportion of light reflects back off the inside surface.
• Because a proportion of the light goes off in other directions in the course of reflection and refraction, the ray loses intensity before it becomes visible to the observer. Anywhere between 2% and 98% can be lost in the process.

#### Some key terms

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 (900), 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.

The refractive index of a medium is the amount by which the speed (and wavelength) of electromagnetic radiation (light) is reduced compared with the speed of light in a vacuum.

• Refractive index (or, index of refraction) is a measure of how much slower light travels through any given medium than through a vacuum.
• The concept of refractive index applies to the full electromagnetic spectrum, from gamma-rays to radio waves.
• The refractive index of a medium is a numerical value and is represented by the symbol n.
• Because it is a ratio of the speed of light in a vacuum to the speed of light in a medium there is no unit for refractive index.
• If the speed of light in a vacuum = 1. Then the ratio is 1:1.
• The refractive index of water is 1.333, meaning that light travels 1.333 times slower in water than in a vacuum. The ratio is therefore 1:1.333.
• As light undergoes refraction its wavelength changes as its speed changes.
• As light undergoes refraction its frequency remains the same.
• The energy transported by light is not affected by refraction or the refractive index of a medium.
• The colour of refracted light perceived by a human observer does not change during refraction because the frequency of light and the amount of energy transported remain the same.

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 (900), 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 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.
###### References

https://en.wikipedia.org/wiki/Reflection_(physics)

• 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 (900), the boundary between two media.
• If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

If one line is normal to another, then it is at right angles. So in geometry, the normal is a line drawn perpendicular to and intersecting another line.

In optics, the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to 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.
• Light travels in a straight line through a vacuum or a transparent medium such as air, glass, or still water.
• If light encounters a force, an obstacle or interacts with an object, a variety of optical phenomena may take place including absorption, dispersion, diffraction, polarization, reflection, refraction, scattering or transmission.
• Optics treats light as a collection of rays that travel in straight lines and calculates the way in which they change direction (deviate) when encountering different optical phenomena.
• When the normal is drawn on a ray diagram, it provides a reference against which the amount of deviation of the ray can be shown.
• The normal is always drawn at right angles to a ray of incident light at the point where it arrives at the boundary with a transparent medium.
• 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.

Refraction refers to the way that electromagnetic radiation (light) changes speed and direction as it travels across the interface between one transparent medium and another.

• As light travels from a fast medium such as air to a slow medium such as water it bends toward the normal and slows down.
• As light passes from a slow medium such as diamond to a faster medium such as glass it bends away from the normal and speeds up.
• In a diagram illustrating optical phenomena like refraction or reflection, the normal is a line drawn at right angles to the boundary between two media.
• A fast (optically rare) medium is one that obstructs light less than a slow medium.
• A slow (optically dense) medium is one that obstructs light more than a fast medium.
• The speed at which light travels through a given medium is expressed by its index of refraction.
• If we want to know in which direction light will bend at the boundary between transparent media we need to know:
• Which is the faster, less optically dense (rare) medium with a smaller refractive index?
• Which is the slower, more optically dense medium with the higher refractive index?
• The amount that refraction causes light to change direction, and its path to bend, is dealt with by Snell’s law.
• Snell’s law considers the relationship between the angle of incidence, the angle of refraction and the refractive indices (plural of index) of the media on both sides of the boundary. If three of the four variables are known, then Snell’s law can calculate the fourth.

Reflection takes place when incoming light strikes the surface of a medium, obstructing some wavelengths which bounce back into the medium from which they originated.

Reflection takes place when light is neither absorbed by an opaque medium nor transmitted through a transparent medium.

If the reflecting surface is very smooth, the reflected light is called specular or regular reflection.

Specular reflection occurs when light waves reflect off a smooth surface such as a mirror. The arrangement of the waves remains the same and an image of objects that the light has already encountered become visible to an observer.

Diffuse reflection takes place when light reflects off a rough surface. In this case, scattering takes place and waves are reflected randomly in all directions and so no image is produced.

Internal reflection takes place when light travelling through a medium such as water fails to cross the boundary into another transparent medium such as air. The light reflects back off the boundary between the two media.

• Internal reflection is a common phenomenon so far as visible light is concerned but occurs with all types of electromagnetic radiation.
• For internal refraction to occur, the refractive index of the second medium must be lower than the refractive index of the first medium. So internal reflection takes place when light reaches air from glass or water (at an angle greater than the critical angle), but not when light reaches glass from air.
• In most everyday situations light is partially refracted and partially reflected at the boundary between water (or glass) and air because of irregularities in the surface.
• If the angle at which light strikes the boundary between water (or glass) and air is less than a certain critical angle, then the light will be refracted as it crosses the boundary between the two media.
• When light strikes the boundary between two media precisely at the critical angle, then light is neither refracted or reflected but is instead transmitted along the boundary between the two media.
• However, if the angle of incidence is greater than the critical angle for all points at which light strikes the boundary then no light will cross the boundary, but will instead undergo total internal reflection.
• The critical angle is the angle of incidence above which internal reflection occurs. The angle is measured with respect to the normal at the boundary between two media.
• The angle of refraction is measured between a ray of light and an imaginary line called the normal.
• In optics, the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to 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 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 (900), 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.
###### References
• 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 (900), the boundary between two media.
• If the boundary between the media is curved, then the normal is drawn at a tangent 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 (900), 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.