Location: Ch 5: Reflection & Refraction
REFLECTION AND REFRACTION 

IN THIS CHAPTER:

  • Reflection
  • The Law of Reflection
  • Mirrors
  • Diffuse Reflection
  • Reflection of Sound
  • Refraction
  • Refraction of Sound and Light
  • Atmospheric Reflection
  • Dispersion in a Prism
  • The Rainbo
  • Total Internal Reflection
W hen a wave reaches a boundary or any rigid object, part of the wave bounces back into the first medium. If a wave is sent along a spring that is secured to a wall, the wave will be sent back as soon as it hits the wall. If the rigid object is replaced with something that is less rigid, some energy is transferred into the new medium but some is still reflected. These waves are partially reflected. Metals such as silver or aluminum are rigid to light waves and therefore look shiny. Thus, silver is used for mirrors. However, this only happens when a wave’s direction is perpendicular to the rigid surface. If it encounters the rigid surface at an angle, it will bounce off at the same angle. These waves can be thought of as a simple ray. The ray that is coming towards the mirror is called the incident ray. This angle and the reflected ray’s angle make equal angles with a line perpendicular to the surface. This line is called the normal. Therefore, the angle of incidence is equal to the angle of reflection. Thus, A incidence = A reflection.
Light reflecting off of red & blue surfaces

    When you look in the mirror, you see an image of yourself in the mirror. When light reflects off you, it goes in an infinite number of directions. These rays are known as divergent rays. When they reflect off the mirror they continue to diverge and they appear to have originated behind the mirror. The image you see in the mirror is called a virtual image because the light does not go there. People’s eyes cannot tell the difference between a mirror and an actual object. There is no difference between light from a mirror and light from an actual object. On a flat mirror, the image also appears to be the same distance that you are from the mirror and also is the same size.

    When light encounters a rough surface it is reflected in various directions. Such a reflection is a diffuse reflection. A surface is considered rough if the elevations in surface are no longer than 1/8 the wavelength. That means that a surface may be polished for one type of wave but not another. Light that hits a page reflects light in many different directions, allowing people to see the page from many distinct angles.

    Echoes are sounds that have been reflected off a rigid surface. Sounds can reflect from all surfaces of a room. The study of the properties of surfaces is known as acoustics. A reverberation is a sound reflecting off a wall. Too many reverberations result in a noisy room and garbled sound. However, absorbent walls make a room sound dull and quiet. Sometimes concert halls have grooves in the walls so a listener hears many small sound waves, rather than one dominant sound wave coming from one direction. Oftentimes reflective discs will be placed above the orchestra to help direct sound to an audience.

    Refraction occurs when one part of a wave is made to travel slower or faster than another part of the wave. Wave fronts can be used to help diagram a wave’s progress through a medium. Wave fronts are always drawn perpendicular to the wave’s direction. Sound waves can be refracted when parts of the wave fronts travel faster than other parts. If the ground is warm, sound near the ground will travel faster than sound in the air.

Wave Front Diagrams of Diffraction
    When light travels through different mediums of different temperatures it tends to bend and change direction. This is refraction of light. Snell’s law is a quantitative law through which we can calculate the index of refraction. Snell’s law states, n sin Q = n' sin Q'. This means that the index of refraction multiplied by the sine of the incident angle equals the index of refraction multiplied by the sine of the refracted angle. When light enters a medium which makes it slow down, the rays bend towards the normal. When light enters a medium which allows it to speed up, the rays bend away from the normal. Light paths are both reversible for reflection and refraction. Thus, if you can see a person in a mirror then they can see you too, even if the mirror is submerged in water.

    An interesting thing happens on hot days when you look at the ground. When you do this, you see a reflection. This reflection is known as a mirage. Mirages are caused by light entering hot air near the ground. The hot air refracts the light upwards until it reaches your eyes. When it reaches your eyes, the brain constructs a virtual image that seems to be coming from below the ground, and thus we see a mirage.

Mirages
    Since the natural frequencies of most objects are in the ultraviolet ranges, violet is slowed down the most when it travels through a material. When light encounters a prism, different colors will be slowed down in different amounts. This slowing down separates white light into the spectrum of colors that it is made up of. Separation of light according to frequency is called dispersion. When the sun is shining in the sky and it is raining somewhere else, sunlight falls upon the raindrops. These water droplets act as small prisms and disperse the sun’s light. If you look at the rain droplets at the correct angle, you can see the spectrum of colors in a rainbow. Rainbows are actually circles but the ground gets in the way of the rainbow and we only see an arc. When sunlight hits a raindrop, the light begins to separate. Some of the light then reflects off the back of the droplet and continues to disperse. If there are many droplets, red and violet light may combine in the middle to produce yellows, greens and blues. However, all this must happen when you look at the rainbow at the right angle. You can see a rainbow if the angle between the rainbow and the sunlight is between 40° and 42°. People do not need to look straight up at 41° to see a rainbow. If you look anywhere along a conical arc swept out at 41°, you will see the rainbow. The cone created by this is a person’s cone of vision for the rainbow. As you move, your cone moves with you. Thus, one can never reach a rainbow.

    There is a certain angle at which light beams will not emerge into the air from another medium. This is the critical angle. If you tip a light source to an angle that is greater than the critical angle the light will be unable to enter the new medium; it will be reflected back. Then the beam is experiencing total internal reflection. When this happens the light will stay trapped in whatever medium it is in until it has an incident angle less than the critical angle. A special case of critical angle is a diamond. Its critical angle is 24.6°. That means that most light that enters is unlikely to escape. When a diamond is cut as a gemstone, light that enters usually is reflected in several directions before it escapes. This is why a diamond flashes unexpectedly. This property of a diamond also disperses the colors and the result is an array of different colors. Fiber optics work in the same way. In a fiber-optic cable, there are thousands of optic fibers. These transparent fibers pipe light from one place to another by way of internal reflections. These fibers can be used for mechanics, physicians and high-speed computer networks.

    In conclusion, reflection results when a wave reaches a boundary between two media and bounces back into the first. Usually part of the wave is reflected and part of it passes into the second. The angles of incidence and reflection are always equal. Flat mirrors form a virtual image of an object. This virtual image is the same size as the original image and it appears to be the same distance that the object is from the mirror. Reflection only occurs on a smooth surface. No reflection occurs if the surface is rough and the light just reflects in many directions. Refraction occurs when waves change direction as they pass into a different medium. The speed of light in materials depends on the frequency of the light, which causes different colors to refract differently and spread out into a visible spectrum. Lastly, light waves are unable to refract and reflect back into the first medium in total internal reflection.
Location: Ch 5: Reflection & Refraction