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Lecture notes, lecture Refraction of Light
Medical Imaging (091403 )
University of Technology Sydney
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PAN supplementary notes Courtesy of Les Kirkup
1
Optics 1
Refraction of light
Serway and Vuille (9th edition), sections 22- 22, 22.
Introduction Many devices and instruments exploit the properties of light. As examples: lasers are used for purposes as diverse as optical communication, holography and attaching retinas. The telescope and microscope create images of distant and near objects respectively permitting us to discern features that would otherwise be hidden to the ‘naked eye’. But what is light and how are we able to ‘manipulate’ light to, for example, produce an image of a distant object or a living cell? In this lecture we will introduce some of the basic phenomena associated with light. We will discover how an understanding of these phenomena can lead to an explanation of instruments such as the endoscope and the compound microscope. We will consider:
- ••• The nature of light
- ••• Reflection and refraction
- ••• Total internal reflection
- ••• Fibre optics
- ••• Dispersion
The nature of light (section 22 of Serway and Vuille) Careful experimentation reveals that light exhibits the properties of both a particle and those of a wave. This is often referred to as ‘wave-particle duality’. For example, light can be diffracted (which is a wave phenomenon which we will deal with in a later lecture). Also a light ‘packet’ can collide with an electron and give up all its energy to the electron – this is an example of a particle property.
An important property of light is its velocity, which depends upon the material (usually termed the ‘medium’) in which it travels. In a vacuum light has a velocity of c = 3 × 108 m/s.
Reflection (section 22 of Serway and Vuille) We often consider a very narrow beam of light, which is referred to as a ray and consider what occurs when a ray strikes a surface (for example glass). If the glass is very smooth the phenomenon of specular reflection occurs. If the surface is rough then diffuse reflection occurs as shown in figure 1.
Specular reflection Diffuse reflection
Figure 1: Specular and diffuse reflection
When a light ray strikes a smooth surface, experiment shows that the angle at which the ray is reflected, θ 1 ' (measured with respect to the normal) is equal to the angle of incidence, θ 1. This is shown in figure 2.
Figure 2: Reflection of light ray
The law of reflection is θ 1 =θ 1 '
Refraction (sections 22 and 22 of Serway and Vuille) When light travels from one medium into another (for example from air to glass) the velocity of the light changes. A consequence of the change in velocity is that the direction that the light travels also changes. This is referred to as refraction. In fact, as light enters glass from air, its velocity decreases.
The index of refraction, n, of a medium is defined as =
speed of light in vacuum speed of light in a medium
=
The index of refraction is a dimensionless number that is equal or greater than 1 because v < c.
PAN supplementary notes Courtesy of Les Kirkup
2
Substance Refractive index Diamond 2. Flint glass 1. Crown glass 1. Water 1.
Table 1: Refractive index for some substances at 20 °C using light with wavelength in a vacuum of 589 nm.
Example 1: What is the speed of light in crown glass? Ans: 2 × 108 m/s
Figure 3: Refraction and reflection of light. θ 2 is the angle of refraction.
We can see that θ 1 <θ 2 i. as the light enters
the glass its direction change so that it travels closer to the normal. By considering the change in velocity that occurs as the light travels from one medium into another, we can show,
2
1 1
2 sin
sin θ
θn
n
n 1 is the refractive index of medium 1 n 2 is the refractive index of medium 2
This is often referred to as Snell’s law.
We can also show that the ratio of the refractive indices is equal to the ratio of the velocities of light in the media, ie,
2
1 1
2 v
v n
n =
where v 1 is the velocity of light in medium 1 where v 2 is the velocity of light in medium 2
Example 2: Light travels from water into diamond. If the angle of incidence of the light
on the surface between water and diamond is 52 °, calculate the angle of refraction. Ans: 25°
Total internal reflection (section 22 of Serway and Vuille) An important effect occurs when light attempts to travel from a medium with a high refractive index to another medium of lower refractive index.
As the angle of incidence increases, the angle of refraction also increases until the angle of refraction reaches 90°. The angle of incidence for which the angle of refraction is 90° is called the critical angle (the symbol used for the critical angle is θc). If the angle of incidence is increased further then all the light is reflected within the first medium. This is referred to as total internal reflection. We can show that,
1
sin 2 n
n θc= where n 1 > n 2.
Example 3: Calculate the critical angle from light travelling from diamond into water (use the data in table 1). Ans: 33
Fibre Optics (see section 22 of Serway and Vuille) Fibre optics exploits the phenomenon of total internal reflection. Only a small amount of light intensity is lost in a fibre due to reflection from the sides of the fibre. Fibre optic based devices have found a wide range of medical application in instruments called endoscopes.
As an exercise, go to the library (or ‘surf’ the Internet) and write about a page on the construction and application of an endoscope used for medical purposes. If you prefer, write a page about any other scientific application of fibre optics.
Dispersion (see section 22 of Serway and Vuille) The refractive index of a medium is not really constant but depends upon the wavelength of the light. Visible light is not a single wavelength but is a ‘continuous spectrum’ consisting of wavelengths from about 0 μm (corresponding to violet) to 0 μm (corresponding to red).
The refractive index decreases as the wavelength increases. This means if we have two rays of light, one violet and one red, that
Lecture notes, lecture Refraction of Light
Course: Medical Imaging (091403 )
University: University of Technology Sydney
