Behavior of Light

Behavior of Light in different materials

The speed of light = 1,080,000,000 kilometers per hour

Light travels in straight lines.

Light comes from natural and human made sources

Objects can be transparent, translucent, or opaque.

Transparent: to show through
Translucent: transmitting and diffusing light so that objects beyond cannot be seen clearly
Opaque: blocking the passage of radiant energy and especially light

Discussion:

The light we are able to see with our eyes is called visible light. This light actually is a combination of different colored light. The different colors of light have different wavelengths and frequencies (and thus different speeds). A prism separates white light into red, orange, yellow, green, blue, indigo, and violet – these lights are called the spectrum. A good way to remember the colors of the spectrum is Roy G. Biv. In a rainbow, the drops of water act like prisms and we see the spectrum of colors.

Absorption

Different colored objects absorb light and heat up in different ways. Light colors reflect more light, but dark colors absorb more light; light colors are cooler, dark are warmer. That is why people wear light clothes in the summer, that is also why asphalt roads get so hot in the summer.

What is one way you can tell that light colored objects reflect more light than dark colored objects?

Colors

Light has a very important role in how we perceive colors. We know what color an object is because of wavelengths of visible light that it reflects. Remember that the spectrum, Roy G. Biv, has different wavelengths; violet has the shortest wavelengths and red has the longest.

In other words we see yellow in a banana because bananas reflect light with the wavelength that makes us see yellow. We see green grass because the grass reflects light with the wavelength that makes us see green.

Reflection of Light:

Objectives:

1. Compare regular and diffuse reflections.

2. Explain how concave and convex mirrors from images.

3. List several uses of concave and convex mirrors.

Resources:

Notes:

Reflection of light:

When light reaches a solid object one of the things that can happen is that the light can be reflected. The reflected light can be either partially or completely reflected based on the elasticity of the material. For this reason, metals make good reflective surfaces.

Law of reflection:

The law of reflection states that the angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal.

(spaceguard.ias.rm.cnr.it/.../dictionary/ img/reflection.gif) / ( 132/132notes/fig201.gif)

This law applies to regular, partial and diffuse reflection.

Regular Reflection:

Regular reflection describes reflection off of very smooth surfaces. It is the type of reflection that can be seen with a mirror or off of a lake on a day without any wind. Here are a few conditions that are true regarding regular reflection.

/ Regular reflection is reflection off of a very smooth opaque surface
/ Angle () of incidence = of reflection
/ The image looks exactly like the object

Diffuse Reflection:

When light is incident off of a rough or irregular surface, it can be defined as irregular of diffuse reflection. This occurs hen you look at the same lake on a windy day.

/ Diffuse reflection is reflection off of a rough or irregular opaque surface
/ Reflected rays are scattered
/ The formed image is not clearly defined
/  of incidence =  of reflection. The difference is that the surface is filled with different angles.

( edition5/reflec4.gif)

Refraction of Light:

Refraction is defined as the bending of light due to a change in its speed. This is why a straw appears bent in a glass of water or why a swimming pool appears shallower than it really is. The differences in the position and dimensions are considered apparent because they have not actually changed. The differences are caused by the changing speed of the light as it transitions to different media.

/ Remember that light (like all waves) travels at constant speed within a medium
/ The speed changes as light changes medium
/ Light travels faster in less dense mediums
/ In less dense mediums the light moves away from the normal
/ Moves slower in more dense mediums
/ In more dense mediums the light moves towards the normal

( refraction-fish.gif)

Index of Refraction:

The index of refraction is a measure of the relative speed change from air to a different medium.The greater the change in speed the greater the index of refraction.

/ Air is given the relative index of 1
/ The higher the speed change the higher the index value
Material / Refractive Index
Air / 1.0003
Water / 1.33
Glycerin / 1.47
Immersion Oil / 1.515
Glass / 1.52
Flint / 1.66
Zircon / 1.92
Diamond / 2.42
Lead Sulfide / 3.91
/

(micro.magnet.fsu.edu/primer/images/ refraction/refangle.jpg)

Electromagnetic waves with wavelengths  in the range of ~400nm to ~750nm are called visible light. We see light because it stimulates the cells in our eyes. Because our eyes are able to distinguish between different wavelength of light we perceive color. If the light reaching our eyes contains a broad mixture of wavelength, we interpret it as white light. Because light is an EM wave, it exhibits several behaviors characteristic of waves such as reflection, refraction and diffraction.

In a homogeneous, isotropic medium light travels in a straight line. When we visually perceive the world around us, we implicitly assume that light follows a straight-line path. But when light encounters a boundary between two media with different indices of refraction, or when it travels through a non-homogeneous or non-isotropic medium, its path may not be a straight line. If we neglect diffraction, then we can analyze the propagation of light through different media by analyzing the path of a light ray. This is called the ray approximation of geometrical optics.

Reflection

Reflection is the abrupt change in the direction of propagation of a wave that strikes the boundary between two different media. At least some part of the incoming wave remains in the same medium. Assume the incoming light ray makes an angle i with the normal of a plane tangent to the boundary. Then the reflected ray makes an angle r with this normal and lies in the same plane as the incident ray and the normal.

Law of reflection: r = i
The angle of reflection equals the angle of incidence.

Specular reflection occurs at smooth, plane boundaries. Then the plane tangent to the boundary is the boundary itself. Reflection at rough, irregular boundaries is diffuse reflection. The smooth surface of a mirror reflects light specularly, while the rough surface of a wall reflects light diffusely.

The reflectivity of a surface material is the fraction of energy of the oncoming wave that is reflected by it. The reflectivity of a mirror is close to 1.

Problem:

/ How many times will the incident beam shown in the figure below be reflected by each of the parallel mirrors?

/ Solution:
After each path between the mirrors the beam gains a distance d in height.
We have d/1m = tan(5o), d = tan(5o)m = 8.75cm. The beam must therefore pass 11 times between the mirrors to gain a height of 1m, 6 times towards the right and 5 times towards the left.

Refraction

Refraction is the change in direction of propagation of a wave when the wave passes from one medium into another, and changes its speed. Light waves are refracted when crossing the boundary from one transparent medium into another because the speed of light is different in different media. Assume that light waves encounter the plane surface of a piece of glass after traveling initially through air as shown in the figure below.

What happens to the waves as they pass into the glass and continue to travel through the glass? The speed of light in glass or water is less than the speed of light in a vacuum or air. The speed of light in a given substance is v = c/n, where n is the index of refraction of the substance. The index of refraction is a material property and in general depends on the wavelength of the light wave. Typical values for the index of refraction of glass are between 1.5 and 1.6, so the speed of light in glass is approximately two-thirds the speed of light in air. The distance between wavefronts will therefore be shorter in the glass than in air, since the waves travel a smaller distance per cycle.

If f is the frequency of the wave and = 1/f is the period, i.e. the time interval between successive crests passing a fixed point in space, then 1 = v1= c/n1 and 2 = v2= c/n2, or

1/2 = n2/n1.

Now consider wavefronts and their corresponding light rays approaching the surface at an angle.

We can see that the rays will bend as the waves pass from air to glass. The bending occurs because the wavefronts do not travel as far in one cycle in the glass as they do in air. As the diagram shows, the wavefront halfway into the glass travels a smaller distance in glass than it does in air, causing it to bend in the middle. Thus, the ray, which is perpendicular to the wavefront, also bends. The situation is like a marching band marching onto a muddy field at an angle to the edge of the field. The rows bend as the speed of the marchers is reduced by the mud. The amount of bending depends on the angle of incidence and on the indices of refraction of glass and air, which determine the change in speed. From the figure we can see that

/2 = sin1/sin2.

But 1/2 = n2/n1. Therefore

n2/n1 = sin1/sin2, or n1sin1 = n2sin2.

This is Snell's law, or the law of refraction.

nisini = ntsint.

When light passes from one transparent medium to another, the rays are bent toward the surface normal if the speed of light is smaller in the second medium than in the first. The rays are bent away from this normal if the speed of light in the second medium is greater than in the first. The picture below shows a light wave incident on a slab of glass.

One part of the wave is reflected, and another part is refracted as it passes into the glass. The rays are bent towards the normal. At the second interface from glass into air the light passing into the air is refracted again. The rays are now bent away from the normal.

Problem:

/ The path of light in air incident on and transmitted through a glass plate is shown in the figure below.

The angle of the incident ray to the normal is 45° and equals that of the reflected ray. The transmitted ray is refracted at an angle of 28° to the normal and exits the glass at an angle of 45° to the normal, an angle equal to that of the incident ray. What is the index of refraction of the glass?
/ Solution:
Snell's law: nisini = ntsint.as the ray enters from the air into the glass, we have ni = 1, i = 45°, and t = 28°. We therefore have nt = nisinsint = sin45°/sin28° = 1.5.

Total internal reflection

When light propagates from air into glass or from glass in to air it may change its direction of travel. Snell's law reveals the relationship between the directions of travel in the two media.

n1sin1 = n2sin2

Consider light propagating in glass with index of refraction n1 = 1.5 towards a glass-air boundary. If the angle the light makes with the normal to the boundary in the glass is 1, then the angle it makes in the air is given by

sin2 = (n1/n2)sin1 = 1.5 sin1.

If sin1 > (1/1.5) = 2/3, or 1 > 41.8o, then sin2 is greater than 1 and there is no solution for 2. The angle c for which sinc = n2/n1 is called the critical angle. For angles greater than the critical angle there exists no solution for 2, and there is no refracted ray. The incident light is totally reflected, obeying the law of reflection. If n2 = 1.5 and n1 = 1 then the critical angle is c = 41.8o.

Total internal reflection occurs only if light travels from a medium of high index of refraction to a medium of low index of refraction. Let light travel from medium 1 into medium 2 and let n1 > n2. Then the critical angle c is given by

sinc = n2/n1

For angles greater than the critical angle the incident light is totally reflected, obeying the law of reflection.

Dispersion

The velocity of light in a material, and hence the index of refraction of the material, depends on the wavelength of the light. The index listed in tables is either an average index, or it is the index for one particular wavelength. Since the refractive index depends on the wavelength of the light, light waves with different wavelengths and therefore different colors are refracted through different angles. This is called dispersion, because white light is dispersed into its component colors while traveling through the material. In general, the index of refraction n varies inversely with wavelength. It is greater for shorter wavelengths.

The table below gives the index of refraction for various wavelengths of light in glass.

Color / Wavelength / Index of Refraction
blue / 434 nm / 1.528
yellow / 550 nm / 1.517
red / 700 nm / 1.510

Snell's law combined with a wavelength-dependent index of refraction nexplains the dispersive properties of a prism. The sides of a prism are not parallel and light changes direction when it passes through it.

A ~1% variation in the index of refraction over the entire visible range of electromagnetic radiation still results in a significant change in the direction of the emerging red and blue rays. Since in general the index of refraction is bigger for shorter wavelengths, blue light gets bent more than red light.

Rainbows

A rainbow is produced by dispersion and internal reflection of light in water droplets in the atmosphere. White light from the sun enters a spherical raindrop. The different colors are refracted through different angles, reflected off the back of the drop, and then refracted again when they emerge from the drop. The white light now has been dispersed into its component colors, and the different colors travel in slightly different directions. You see red light coming from water droplets higher in the sky than violet light. The other colors are found between these, making a rainbow. In the figure below, red light arrives at the eye of the observer from the upper drop and violet light from the lower drop. Other raindrops yield the other colors.

Rainbows are usually seen as half circles. From a plane or from a very tall building or mountain, however, one can see a complete circle. Sometimes one can see a double rainbow. The second, dimmer, band, which is higher in the sky than the first, comes from light reflected twice inside a raindrop. This reverses the order of the colors in the second band.

Sunlight

Sunlight originates at the outer surface of the sun, in a region called the photosphere. This region has a temperature of ~5800oC. The distribution of wavelength in sunlight is determined by the temperature of the photosphere. Not all sunlight is visible. EM waves in the infrared and ultraviolet part of the EM spectrum are also produced in the photosphere.

Sunlight travels from the Sun to the Earth through empty space with the speed of light c. When it enters the earth atmosphere it is refracted. The index of refraction of air near sea level is only 1.0003, so the refraction is barely noticeable. Air molecules, water molecules and dust also scatter some of the light (Rayleigh scattering). These particles scatter shorter wavelength light more efficiently that longer wavelength light. Scattering by tiny particles is always most efficient when the wavelength of the EM wave approximately matches the size of the tiny particle. The dimensions of the molecules and dust particles are much smaller than the wavelengths of visible light, so blue light with the shortest wavelength provides the best match. Blue light is scattered more than red light. Most sunlight travels directly to our eyes, but the scattered light reaches us by a more complicated path from different directions.