Conceptual Physics Chapter 291 Chapter 29 Reflection

Conceptual Physics Chapter 29

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Chapter 29 ReflectionChapter 29 Reflection


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ReflectionReflection

¤ When any type of wave reaches any type of boundary (change in medium), some of the wave energy is transmitted into the new medium and some of the energy is reflected back into the original medium.

¤ Wave energy can be reflected from a boundary in one of two ways – inverted or erect.


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Reflection from a Fixed EndReflection from a Fixed End

¤ When a wave pulse in a rope or spring reaches a fixed end (e.g., the end is securely fastened to a wall) the wave energy will be almost totally reflected and the wave will get inverted (flipped upside-down).

¤ There is no change in the speed of the reflected wave since there is no change in the medium.

¤ There is very little change in the amplitude of the reflected wave since most of the energy is reflected.


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¤ If instead of being secured to a wall, a rope is attached to a heavier rope, a larger portion of the wave energy will now be transmitted leaving less energy to be reflected back into the original medium. The reflected pulse is still inverted when it encounters the more rigid medium.


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Reflection from a Free EndReflection from a Free End

¤ When a wave pulse in a rope or spring reaches a free end (e.g., the end is tied to a massless ring free to slide up and down on a frictionless vertical pole) the wave energy will be almost totally reflected and the wave will remain erect.

¤ There is no change in the speed of the reflected pulse and a negligible change to the amplitude of the wave.


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¤ When a wave pulse originates in a heavy rope and travels into a lighter rope, much of the wave energy will be transmitted leaving little energy to be reflected back into the original medium. The reflected pulse remains erect when it encounters the less rigid medium.


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Reflection of LightReflection of Light

¤ Metal surfaces appear very rigid to light waves. Consequently, most of the light that falls on these surfaces is reflected (and the rest is absorbed) giving metals their shiny appearance.

¤ Glass and water are not as rigid to light waves and these surfaces reflect very little of the light that is incident on them. Most of the light that falls on water or glass is transmitted.


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Law of ReflectionLaw of Reflection

¤ When wave energy (including light waves) reaches a boundary at an angle, it will reflect from the boundary in accordance with the law of reflection.

¤ The angle made by the incident ray and the normal (angle of incidence) is equal to the angle made by the reflected ray and the normal (angle of reflection).


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Diffuse vs Specular Reflection


¤ When parallel rays of light from a distant source approach a perfectly smooth surface (like a mirror), each individual ray will obey the law of reflection causing all reflected rays to remain parallel to one another. This specular reflection creates a clear reflected image.

¤ When the same parallel rays of light approach an uneven or rough surface (like the floor), each individual ray will still obey the law of reflection. This diffuse reflection causes the light rays to be scattered in many different directions.


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¤ If the differences in elevations in a surface are small (less than about one eighth the wavelength of the light that falls on it), the surface is considered smooth and it will generate specular reflection.

¤ A surface may appear smooth for long wavelengths, but rough for short wavelengths.

¤ Whether a surface is a diffuse reflector or a specular reflector depends on the wavelength of the waves it reflects.


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Plane MirrorsPlane Mirrors

¤ Light reflecting from a plane mirror produces a virtual image (a virtual image does not really exist).

¤ The reflected rays diverge from the mirror face and appear to originate from a point located behind the mirror.

¤ The image is erect (or upright), the same size as the object, and is located just as far behind the mirror as the object is in front of the mirror.


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Plane MirrorsPlane Mirrors

What is the minimum height of a plane mirror required in order for a man to see himself from head to toe?


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Curved MirrorsCurved Mirrors

¤ The virtual image formed by a convex mirror (a mirror that curves outward) is smaller and closer to the mirror than the object is.

¤ When an object is close to a concave mirror (a mirror that curves inward), the virtual image is larger and farther away than the object is.

¤ The law of reflection holds for curved mirrors. However, the sizes and distances of object and image are no longer equal.


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Reflection of SoundReflection of Sound

¤ Sound waves obey the law of reflection.¤ An echo is reflected sound. ¤ More sound energy is reflected from a

rigid and smooth surface than from a soft and irregular surface.

¤ Sound energy not reflected is absorbed or transmitted.


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¤ When walls are too reflective, the sound becomes garbled because of multiple reflections of sound waves called reverberations.

¤ When the reflective surfaces are more absorbent, the sound level is lower, and the hall sounds dull and lifeless.

¤ In the design of an auditorium or concert hall, a balance between reverberation and absorption is desired.


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¤ The walls of concert halls are often designed with grooves so that the sound waves are diffused.

¤ A person in the audience receives a small amount of reflected sound from many parts of the wall.


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RefractionRefraction

¤ When a wave that is traveling at an angle changes its speed upon crossing a boundary between two media, it bends.

¤ Refraction is the bending of a wave as it crosses the boundary between two media at an angle.


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The wheel that first meets the lawn slows down first. The axle pivots, and the path bends toward the normal.When both wheels reach the grass, it continues in a straight line at reduced speed.

¤ This is similar to when the front wheels of a toy car roll from a smooth sidewalk on to the lawn.

¤ If the wheels encounter the boundary at an angle, the car will be deflected from its straight-line course.


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¤ The incident ray (which indicates the direction of the wave travel) is perpendicular to the wave front it intersects.

¤ Water waves travel faster in deep water than in shallow water.

¤ When a wave approaches a boundary between deep water and shallow water at an angle, it slows down, the wavelength is reduced and the wave refracts toward the normal.


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¤ Changes in the speed of light as it passes from one medium to another, or variations in the temperatures and densities of the same medium, cause refraction of light.


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¤ When light rays enter a medium in which their speed decreases, as when passing from air into glass, the rays bend toward the normal.

Wave fronts that enter the glass first are the first to slow down.The refracted ray of light is closer to the normal than is the incident ray.


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¤ When light rays enter a medium in which their speed increases, such as from glass into air, the rays bend away from the normal.

Wave fronts that enter the air first are the first to speed up.The refracted ray of light is further from the normal than is the incident ray.


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¤ How much the light waves will speed up or slow down when they enter a new medium is dependant on the index of refraction, n, of the medium.

¤ The index of refraction describes the optical density or how often photons of light interact with atoms in the medium.

vc

medium the in light of speedvacuum a in light of speed

n


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¤ A vacuum has an index of refraction of exactly 1.0 while air has an index of refraction of approximately 1.0


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¤ How much the light will bend towards or away from the normal line upon refraction can be determined by Snell’s law

2211 θsinn=θsinn


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¤ The laser beam bends toward the normal when it enters the water, and away from the normal when it leaves.

¤ The light paths are reversible for both reflection and refraction.


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¤ The fish appears to the boy to be closer than it actually is.


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DispersionDispersion

¤ Different frequencies of light travel at different speeds in transparent materials so they bend at different angles.

¤ The separation of light into colors arranged according to their frequency is called dispersion.


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DispersionDispersion

Dispersion of sunlight by a water drop produces a rainbow.As the ray of sunlight enters a spherical raindrop near its top surface, some of the light is refracted.

• The light is dispersed into its spectral colors. Violet is bent the most and red the least.

• At the opposite part of the drop, rays are partly reflected back into the water.

• Some rays are refracted into the air. This second refraction is similar to that of a prism.

• Refraction at the second surface increases the dispersion produced at the first surface.


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Total Internal ReflectionTotal Internal Reflection

When light passes from water into air, the light is partly refracted and partly reflected at the interface. As the angle of incidence increases, the angle of refraction increases.


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At the critical angle, the emerging beam skims the surface.


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Past the critical angle, there is total internal reflection.Total internal reflection is as the name implies —100% reflection.

This is a condition that only comes about when light approaches a boundary from a slower medium to a faster medium.

The critical angle for water is about 49°. This means that within the water, rays of light that are more than 49° from the normal will be totally internally reflected.


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¤ Since mirrors typically reflect only 90 to 95% of incident light, prisms are often used instead of mirrors in many optical instruments.


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¤ The brilliance of diamonds is a result of their very small critical angle and total internal reflection.

¤ With a critical angle of just 24.6°, light inside a diamond is far more likely to be totally internally reflected than to escape.

¤ All light rays more than 24.6° from the normal to a surface in a diamond are kept inside by total internal reflection.


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¤ Optical fibers, sometimes called light pipes, are transparent fibers that pipe light from one place to another.

¤ They do this by a series of total internal reflections.

¤ Optical fibers are important in communications, replacing bulky and expensive copper cables to carry telephone messages.

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Conceptual Physics Chapter 291 Chapter 29 Reflection