# Law of Refraction Explained

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The diagram deals with the Law of Refraction (Snell’s law) and explains how to use the equation to predict what will happen to the direction in which light travels when it crosses the boundary between two transparent media.

The law defines the relationship between the angle of incidence and angle of refraction of a ray of light with reference to the refractive indices of both media. It can be stated as follows:

When electromagnetic radiation (light) of a specific wavelength crosses the interface of any given pair of media, the ratio of the sines of the angles of incidence and the sines of the angles of refraction is a constant in every case.

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## Description

#### Law of Refraction Explained

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Index of refraction is the other term used for refractive index.
When light crosses a boundary into a medium with a high refractive index (eg. diamond = 2.42) there is a significant change in direction and speed. When light crosses a boundary into a medium with a low refractive index (eg. water = 1.333) there is a less significant change in direction or speed.
In mathematics, the sine of an angle in a right-angle triangle is the ratio produces by dividing the length of 'a' by the length of 'b': the length of the side opposite the angle the length of the longest side (the hypotenuse)
Refraction refers to the way light changes both direction and speed as it travels from one transparent medium into another.

Have you already checked out An Introduction to Reflection, Refraction and Dispersion?

It is the opening page of our Reflection, Refraction and Dispersion Series and contains masses of useful information. This is the table of contents:

• This page explains how to use the law of refraction (also called Snell’s law).
• Related terms, including reflection, refraction and chromatic dispersion are covered on earlier pages of this series.
• An introduction to term refractive index and how the refractive index of a transparent medium is used also appears in the series.

An overview of refraction

• Refraction refers to the way that light (electromagnetic radiation) changes speed and direction as it travels from one transparent medium into another.
• Refraction takes place as light travels across the boundary between different transparent media and is a result of their different optical properties.
• Refraction is the result of the differences in the optical density of transparent media. Gases have a very low optical density whilst diamonds have a high optical density.
• When light is refracted its path bends and so changes direction.
• The effect of refraction on the path of a ray of light is measured by the difference between the angle of incidence and the angle of reflection.
• As light travels across the interface between different media it changes speed.
• Depending on the media through which light is refracted, its speed can either increase or decrease.

An overview of refraction and wavelength

• Every wavelength of light is affected to a different degree when it encounters a medium and undergoes refraction.
• Every wavelength of light changes both speed and direction by a different amount when it encounters a new medium and undergoes refraction.
• The change in angle for any wavelength of light undergoing refraction within a specific transparent medium can be predicted if the refractive index of the medium is known.
• The refractive index for a medium is calculated by finding the difference between the speed of light in a vacuum and its speed as it travels through the medium.
Colour wavelength (nm) Refractive index
Red 640 1.50917
Yellow 589 1.51124
Green 509 1.51534
Blue 486 1.51690
Violet 434 1.52136

The refractive index for crown glass is often given as being 1.52. This table shows how that figure alters with wavelength

The diagram

This diagram deals with the Law of Refraction (Snell’s law) and explains how to use the equation to predict what will happen to the direction in which light travels when it crosses the boundary between two transparent media. The law defines the relationship between the angle of incidence and angle of refraction of a ray of light with reference to the refractive indices of both media. It can be stated as follows:

When electromagnetic radiation (light) of a specific wavelength crosses the interface of any given pair of media, the ratio of the sines of the angles of incidence and the sines of the angles of refraction is a constant in every case.

• Snell’s law deals with the fact that for an incident ray of light approaching the boundary of two media, the sine of the angle of incidence multiplied by the index of refraction of the first medium is equal to the sine of the angle of refraction multiplied by the index of refraction of the second medium.
• Snell’s law deals with the fact that the sine of the angle of incidence to the sine of the angle of refraction is constant when a light ray passes across the boundary from one medium to another.
• Snell’s law can be used to calculate the angle of incidence or refraction associated with the use of lenses, prisms and other everyday materials.
• When using Snell’s law, the angles of incidence and refraction are measured between the path of a ray of light and the normal.
• 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.
• The speed of light in a vacuum expressed in metres per second = 299,792,458 m/sec. So = 299,792 km/sec.

#### 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 (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 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.

In physics and optics, a medium refers to any material (plural: media) through which light or other electromagnetic waves can travel. It’s essentially a substance that acts as a carrier for these waves.

• Light is a form of electromagnetic radiation, which travels in the form of waves. These waves consist of oscillating electric and magnetic fields.
• The properties of the medium, such as its density and composition, influence how light propagates through it.
• Different mediums can affect the speed, direction, and behaviour of light waves. For instance, light travels slower in water compared to a vacuum.
• Examples of Mediums:
• Transparent: Materials like air, glass, and water allow most light to pass through, with minimal absorption or scattering. These are good examples of mediums for light propagation.
• Translucent: Some materials, like frosted glass or thin paper, partially transmit light. They allow some light to pass through while diffusing or scattering the rest.
• Opaque: Materials like wood or metal block light completely. They don’t allow any light to travel through them.
• The permittivity (electrical response) and permeability (magnetic response) of a medium determine how light interacts with it. These properties influence factors like:
• Refraction: Bending of light as it travels from one medium to another with different densities.
• Reflection: Bouncing back of light when it encounters a boundary between mediums.
• Absorption: Light being captured and converted into other forms of energy (like heat) by the medium.
###### References
• In physics and optics, a medium refers to any material through which light or other electromagnetic waves can travel. It’s essentially a substance that acts as a carrier for these waves.
• Light is a form of electromagnetic radiation, which travels in the form of waves. These waves consist of oscillating electric and magnetic fields.
• The properties of the medium, such as its density and composition, influence how light propagates through it.
• Different mediums can affect the speed, direction, and behaviour of light waves. For instance, light travels slower in water compared to a vacuum.
• Examples of Mediums:
• Transparent: Materials like air, glass, and water allow most light to pass through, with minimal absorption or scattering. These are good examples of mediums for light propagation.
• Translucent: Some materials, like frosted glass or thin paper, partially transmit light. They allow some light to pass through while diffusing or scattering the rest.
• Opaque: Materials like wood or metal block light completely. They don’t allow any light to travel through them.

The speed (or velocity) of a light wave is a measurement of how far it travels in a certain time.

• The speed of light is measured in metres per second (m/s).
• Light travels through a vacuum at 300,000 kilometres per second.
• The exact speed at which light travels through a vacuum is 299,792,458 metres per second.
• Light travels through other media at lower speeds.
• A vacuum is a region of space that contains no matter.
• Matter is anything that has mass and occupies space by having volume.
• When discussing electromagnetic radiation the term medium (plural media) is used to refer to anything through which light propagates including empty space and any material that occupies space such as a solid, liquid or gas.
• In other contexts empty space is not considered to be a medium because it does not contain matter.

A nanometre is a unit of measurement of the wavelength of electromagnetic radiation.

• Nanometres are particularly useful when specifying the wavelength of electromagnetic waves in the visible region of the electromagnetic spectrum.
• The visible spectrum ranges from around 400 to 700 nm.

Wavelength is a measurement from any point on the path of a wave to the same point on its next oscillation. The measurement is made parallel to the centre-line of the wave.

• The wavelength of an electromagnetic wave is measured in metres.
• Each type of electromagnetic radiation, such as radio waves, visible light and gamma waves,  forms a band of wavelengths on the electromagnetic spectrum.
• The visible part of the electromagnetic spectrum is composed of the range of wavelengths that correspond with all the different colours we see in the world.
• Human beings don’t see wavelengths of visible light, but they do see the spectral colours that correspond with each wavelength and the other colours produced when different wavelengths are combined.
• The wavelength of visible light is measured in nanometres. There are 1,000,000,000 nanometres to a metre.
• In the field of optics, diffusion refers to situations that cause parallel rays of light to spread out more widely.  When light undergoes diffusion it becomes less concentrated.Diffuse reflections occur when light scatters off rough or irregular surfaces.
• When microscopic features on a surface are significantly larger than the individual wavelengths of light within the visible spectrum, each wavelength of light encounters bumps and ridges exceeding their size.
• Instead of reflecting neatly in one direction, the light scatters in different directions.
• In this case, scattering doesn’t happen completely randomly. The surface features influence the direction of the scattered light, depending on the angle of incidence and the specific bumps and ridges it encounters.
• This scattering creates diffuse reflections, responsible for the soft, uniform illumination seen on textured surfaces like matte paint or unpolished wood.
• In the case of a matte phone screen, for example, the light doesn’t form a clear reflection of your face but rather creates a soft, hazy glow due to the diffused light.

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.

In mathematics, the sine is a trigonometric function of an angle.

• The sine of an acute angle is defined in the context of a right-angle triangle.
• For any specified angle, it’s sine is the ratio of the length of the side opposite that angle, to the length of the longest side of the triangle (the hypotenuse).
• The mathematical notation for sine is sin.

Optical density is a measurement of the degree to which a refractive medium slows the transmission of light.

• The optical density of a medium is not the same as its physical density.
• The more optically dense a medium, the slower light travels through it.
• The less optically dense (or rare) a material is, the faster light travels through it.
• A vacuum has the least optical density and so light travels through it at a maximum speed of 299,792 kilometres per second.
• Optical density accounts for the variation in refractive indices of different media.

https://en.wikipedia.org/wiki/Absorbance