# Reflection & Refraction – Curved Boundary

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The diagram shows an incident ray of light approaching the boundary between air and glass.

• When the ray strikes the boundary between air and glass some of the light bounces off the surface of the glass because it is highly reflective.
• The diagram demonstrates that the angle of incidence and angle of reflection are the same.
• The angles of incidence and reflection are both measured between the ray and the normal (the dotted green line).
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## Description

#### Reflection & Refraction - Curved Boundary

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
_x000D_ _x000D_ A medium is any transparent material through which an electromagnetic wave propagates (plural media).
Refraction refers to the way light changes both direction and speed as it travels from one transparent medium into 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.
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.

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 provides an introduction to a situation in which both reflection and refraction take place at a curved boundary between two transparent media.
• It looks at the path of white light rather than at the paths of the different wavelengths that white light contains.
• Related topics including dispersion are covered on other pages of this series.
• Introductions to the terms refractive index and the law of refraction (sometimes called Snell’s law) also appear on later pages in the series.

An overview of reflection

• Reflection takes place when incoming light strikes the surface of a medium and the light bounces off and returns into the medium from which it originated.
• Reflection takes place when light is neither absorbed by an opaque medium nor transmitted through a transparent medium.

An overview of refraction

• Refraction refers to the way that light (electromagnetic radiation) changes direction and speed 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.
• 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 (such as between air and glass) it changes speed.
• Depending on the media through which light is refracted, its speed can increase or decrease.

An overview of reflection and refraction

• When light strikes the boundary between two different media it may be partially reflected and partially refracted.
• If both reflection and refraction take place:
• A proportion of the light bounces off the surface of the new medium it encounters and returns into the medium from which it originated.
• A proportion crosses the boundary and undergoes refraction, so changes speed and direction.

The diagram

The diagram shows an incident ray of light approaching the curved boundary between air and glass.

• When the ray strikes the boundary between air and glass partial reflection and partial refraction takes place. This means that a proportion of the light bounces off the surface of the glass and returns into the air whilst the rest undergoes refraction.
• When incident light strikes a curved surface the normal is drawn at a tangent to the curve.
• In geometry, a tangent to a curve is a straight line that touches but does not intersect the curve at that point. It can be defined as a line through a pair of infinitely close points on a curve.

Reflection takes place when incoming light strikes the surface of a medium, some wavelengths are obstructed, and the wavefront bounces off and returns into the medium from which it originated.

• The laws of reflection are as follows:
• The incident ray, the reflected ray and the normal all lie in the same plane.
• The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes with the same normal.
• The reflected ray and the incident ray are on the opposite sides of the normal.
• Reflection takes place when light is neither absorbed by an opaque medium nor transmitted through a transparent medium.

Types of reflection

• When sunlight strikes window glass, some light is reflected and some is transmitted through the glass into the room beyond.
• The type of glass made for picture framing is designed to reflect some wavelengths and to transmit others.
• When light illuminates objects and then goes on to strike a mirror, the reflected image can be seen by an observer.
• A reflected image contains objects that we recognise and is made up of visible wavelengths of light and their corresponding colours.
• If a reflecting surface is very smooth, light waves remain in the same order as they bounce off the surface, producing a specular reflection.
• A diffuse reflection, in which no image is visible, results from light reflecting off a rough surface and light waves scattering in all directions.
• Reflection is independent of the optical density of the medium through which incident light travels or of the medium it bounces off.

• When light crosses the boundary between two different transparent media it undergoes refraction.
• The effect of refraction is that light changes speed along with its direction of travel.
• The result of the change in direction is that rays either bend towards or away from the normal.
• As the speed of light changes so does its wavelength but frequency and so the colour an observer sees remains the same.
• The normal is an imaginary line drawn on a ray diagram at right angles (perpendicular) to the boundary between two media.
• The change between the angle of incidence and the angle of refraction of a ray of light is always measured between the ray and the normal.
• Whether light bends towards or away from the normal depends on the difference in optical density of the new medium it encounters.
• An incident ray of light is refracted towards the normal and slows down when it travels from air into glass. Compared with air, glass is a slower, more optically dense medium (with the higher refractive index).
• An incident ray of light is refracted away from the normal and speeds up when it travels from glass into air. Compared with glass, air is a faster, less optically dense medium (with a lower refractive index).

Calculating the angle of refraction

• The direction in which a ray bends, and the precise angle, can be calculated if the type and refractive indices of both media are known.
• The effect of refraction can be calculated using a neat little equation called the law of refraction (also known as Snell’s law).
• If three of the variables are known, the law of refraction can be used to calculate the fourth.
• Tables of refractive indices are available for common materials so that the change in direction of a ray can be calculated.
• Tables of refractive indices for common materials often provide both the refractive index for white light as well as indices for specific wavelengths.

For an explanation of the refractive index (index of refraction) of a medium see: Refractive Index Explained.

For an explanation of how to use the refractive index of a medium see: How to Use the Refractive Index of a Medium.

For an explanation of the Law of Refraction see: Snell’s Law of Refraction Explained.

#### 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 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.

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.

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 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.

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.

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 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 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 tangent to a circle is a straight line that touches but does not intersect the circle and is at right angles to a radial line drawn from  the centre of the circle.

• In geometry, a tangent (or tangent line) to a curve is a straight line that touches but does not intersect the curve. It can be defined as a line through a pair of infinitely close points on a curve.

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

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