Reflection & Refraction – Curved Boundary

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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:

• Introducing reflection
• Types of reflection
• Introducing refraction
• Calculating the angle of refraction
• Introducing chromatic dispersion
• Introducing refraction and wavelength

Overview of this page

• 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.

More about reflection

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.

More about refraction

• 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.