Shinwari,Mariam,Ivan text:

Law of Reflection

Contents

1. #Reflection
2. #Total Internal Reflection
3. #Dispersion
4. #Refraction
5. #References

Reflection

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Reflection Reflection

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"Reflection is a change in direction of a wave upon striking the interface between two materials."(#1.)Reflection is the change in direction of a wave front at an interface between two different media so that the wave front returns into the medium from which it originated. Common examples include the reflection of include the reflection of light, sound and water waves.

meaning When a ray of light strikes a plane mirror, the light ray reflects off the mirror. Reflection involves a change in direction of the light ray. The convention used to express the direction of a light ray is to indicate the angle which the light ray makes with a normal line drawn to the surface of the mirror. The angle of incidence is the angle between this normal line and the incident ray; the angle of reflection is the angle between this normal line and the reflected ray. According to the law of reflection, the angle of incidence equals the angle of reflection. These concepts are illustrated in the diagram below. Image Removedimage 1.

. Image Added

Fig. 1. Reflection (#2.)

In the diagram

Fig. 2. Reflection (#3.)

In image 2, the ray of light approaching the mirror is known as the incident ray (labeled I in the diagram). The ray of light that leaves the mirror is known as the reflected ray (labeled R in the diagram). At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. This line is known as a normal line (labeled N in the diagram). The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection. (These two angles are labeled with the Greek letter "theta" accompanied by a subscript; read as "theta-i" for angle of incidence and "theta-r" for angle of reflection.) The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.In fact, reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index. In the most general case, a certain fraction of the light is reflected from the interface, and the remainder is refracted. Solving Maxwell's equations for a light ray striking a boundary allows the derivation of the Fresnel equations, which can be used to predict how much of the light is reflected, and how much is refracted in a given situation. Total internal reflection of light from a denser medium occurs if the angle of incidence is above the critical angle.It is common to observe this law at work in a Physics lab such as the one described in the previous part of Lesson 1

. To view an image of a pencil in a mirror, you must sight along a line at the image location. As you sight at the image, light travels to your eye along the path shown in the diagram below. The diagram image 3 shows that the light reflects off the mirror in such a manner that the angle of incidence is equal to the angle of reflection.

Fig. 3. Reflection of Light (#3.)

It just so happens that the light that travels along the line of sight to your eye follows the law of reflection. (The reason for this will be discussed later in Lesson 2). If you were to sight along a line at a different location than the image location, it would be impossible for a ray of light to come from the object, reflect off the mirror according to the law of reflection, and subsequently travel to your eye. Only when you sight at the image, does light from the object reflect off the mirror in accordance with the law of reflection and travel to your eye. This truth is depicted in the diagram image 4 below.

Fig. 4. True Image (#3.)

For example, in Diagram A aboveimage 4, the eye is sighting along a line at a position above the actual image location. For light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is less than the angle of reflection. In Diagram B above, the eye is sighting along a line at a position below the actual image location. In this case, for light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is more than the angle of reflection. Neither of these cases would follow the law of reflection. In fact, in each case, the image is not seen when sighting along the indicated line of sight. It is because of the law of reflection that an eye must sight at the image location in order to see the image of an object in a mirror.

Total Internal Reflection

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Total Internal Reflection Total Internal Reflection

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is a phenomena which occurs when light propagates from the medium with greater index of refraction in the medium with lower index of refraction. From Snell's law we know that the light in this case refracts away from the normal. That means that there is an angle of incidence for incoming ray where all the light will not leave the medium with higher index of refraction, but instead it will reflect in direction perpendicular to the normal (i.e. in the plane of the boundary).  If the angle of incidence is larger than this critical angle, all the light is reflected back into the medium with higher index of refraction. We can obtain value for critical angle mathematically using following equation: 

Where n2 is index of refraction of the medium with higher lower index. 

Image of multiple Fig. 5. Multiple total internal reflections (#4.)

courtesy of Wikipedia.

Practical Use of Total Internal Reflection

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Total internal reflection has many practical uses. The best known are arguably its use in glass prisms in binoculars and cameras where it allows for compact size of the instrument while providing for long internal optical paths. Second major area of application is in optical cables - namely in multimode optical cables. There the pure glass/silica core is made of material with higher refractive index than the cladding that surrounds it and so the light which enters it under angle of incidence larger than critical it will reflect there and back thorough the cable to the other end (in the same way as on the picture above). This is used extensively in data communications as optical cables offer higher bandwidth (lower attenuation of high frequency signals), resistance to electromagnetic noise and (much) thinner cables. Optical cables are also used in endoscopes (stomach sonds). Other uses are for example in inkless fingerprint readers. 

In daily life it is easy to demonstrate total internal reflection for example by looking upwards when underwater - you will be able to see a cone of your surroundings (areas where angle of incidence is lower than critical) and reflection of other underwater object everywhere else (where angle of incidence is higher than critical). In other (much simplified) words: when underwater the water surface will in some cases work as a mirror (due to total internal reflection). 

Dispersion of Light

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Dispersion Dispersion

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The index of refraction of medium is dependent on the frequency of incoming light ray. Therefore if light with with wide frequency spectrum (such as daylight) enters for example glass prism, the component frequency bands (for visible colors) will diffract under slightly different angles. The result is light divided into colorful "strip" for each of basic colors. The very same effect is behind rainbow which is natural occurrence of dispersion. 

Fig. 6. Diffraction of light in prism courtesy Wikipedia: (#5.)

Practical Use of Dispersion

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Dispersion is used in spectrometers - devices which are used in many fields of science to analyze the chemical composition of objects. It is based on the fact that different chemical elements emit and absorb different wavelenghts of light, and this spectra can be seen using spectrometers. 

In other fields, the dispersion can be a nuisance: in camera lenses it leads to chromatic aberration and in optical cables chromatic dispersion limits the maximum bandwidth of the fiber (though this effect is not as strong as modal dispersion which is caused by longer paths of reflected rays as opposed to those that travel straight through along the core. 

Refraction

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Refraction Refraction

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It’s the change in direction of a wave due to a change in its medium. It is essentially a surface phenomenon. This is most commonly observed when a wave passes from one medium to another at any angle other than 90° or 0°. (#6.)
Explanation:

Refraction  Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth(#6.). With light, the speed in transparent medium is lower than in vacuum since light can travel in vacuum and doesn’t need a medium to travel.

We characterize the transparent medium by its Index of Refraction, defined as the ratio of the speed of light c in vacuum to the speed on light in the medium:

n=c/v    (index of refraction)      eq….11 (#7.)

n is always 1 or greater depending upon the medium. The index of refraction for some familiar substances:

• Vacuum, defined as 1
• Air, approximately 1.0008
• Water, 1.33
• Glass, 1.5
• Diamond, 2.2

The index of refraction is a way of expressing how optically dense a medium is. The actual index of refraction (other than in a vacuum) depends on the incoming wavelength. Different wavelengths have slightly different speeds in (non-vacuum) mediums. For example, red slows down by a certain amount, but violet slows down by a slightly lower amount - meaning that red light goes through a material (glass, for example) a bit faster than violet light. Red light exits first(#9.).

When wave enters from one medium to another, the wave speed changes but the frequency of the wave remains the same, meaning that the speed of wave depend upon the change in wavelength according to the formula    v=fλ                  eq….2.

After comparing equation 1 and 2 we get λ=c/nf and since c and f don’t change, the wavelength is inversely proportional to n.

 Refraction Refraction is described by Snell's law, which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence θ₁ and angle of refraction θ₂ is equivalent to the ratio of phase velocities (v₁ / v₂) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n₂ / n₁)(#6.):

(#6.)

Fig. 7. Refraction (#6.)

Common Example:

Going from a medium of lower refractive index, to a medium of higher refractive index, the beam bends toward the normal. In opposite case, when light travels from a higher refractive index to lower refractive index, the beam bends away from the normal.

Further Reading/Watching

Fig. 8. Refraction of light in water (#8.)

Related Videos:

• First video explains shortly speed of light in different mediums.
• Second video gives a brief description of how and why refraction happens.

References:

<ac:structured-macro ac:name="anchor" ac:schema-version="1" ac:macro-id="8443a567-ae50-4bbf-8b78-bb3c125956ed"><ac:parameter ac:name="">3.</ac:parameter></ac:structured-macro> 3. _Reflection and Its Importance_. (n.d.).  Retrieved December 10, 2012, from Physics Classroom: \[http://www.physicsclassroom.com/class/refln/u13l1c.cfm\]

4. Total internal reflection. (2012, December 10). Retrieved December 10, 2012, from Wikipedia: http://en.wikipedia.org/wiki/Total_internal_reflection

5. Prism (optics). (2012, December 8). Retrieved December 10, 2012, from Wikipedia: http://en.wikipedia.org/wiki/Prism_%28optics%29

6. Refraction. (2012, December 6). Retrieved December 10, 2012, from Wikipedia: http://en.wikipedia.org/wiki/Refraction

7. Wolfson, R. (2007). Essential University Physics (First ed., Vol. 2). San Francisco, California, United States of America: Pearson Education Inc.

8. Nave, R. (n.d.). Refraction of Light by Water. Retrieved December 10, 2012, from Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr2.html#c1

9. Lally, S. (2012, October 25). Reflection and Refration . Retrieved December 10, 2012, from How Things Work - Towson University Physics 103: http://howthingsworkclass.blogspot.fi/2012/10/reflection-and-refration-reflection.html

#Back to top1. The speed of light in a glass