Angle ofrefraction

First lets consider a double convex lens. Suppose that several rays of light approach the lens; and suppose that these rays of light are traveling parallel to the principal axis. Upon reaching the front face of the lens, each ray of light will refract towards the normal to the surface. At this boundary, the light ray is passing from air into a more dense medium (usually plastic or glass). Since the light ray is passing from a medium in which it travels fast (less optically dense) into a medium in which it travels relatively slow (more optically dense), it will bend towards the normal line. This is the FST principle of refraction. This is shown for two incident rays on the diagram below. Once the light ray refracts across the boundary and enters the lens, it travels in a straight line until it reaches the back face of the lens. At this boundary, each ray of light will refract away from the normal to the surface. Since the light ray is passing from a medium in which it travels slow (more optically dense) to a medium in which it travels fast (less optically dense), it will bend away from the normal line; this is the SFA principle of refraction.

Refractive index of glass

The above diagram shows the behavior of two incident rays traveling through the focal point on the way to the lens. Note that the two rays refract parallel to the principal axis. A second generalization for the refraction of light by a double convex lens can be added to the first generalization.

References: Chomsky, (1959). A review of B. F. Skinner’s Verbal behavior. Language, 35, 26–58. Chomsky,  (1986).  Knowledge  of  language:  Its  nature, origin, and use. New York: Praeger. Lenneberg,  (1967).  Biological  foundations  of  language. New York: Wiley. Noam Chomsky  home  page,  http://web.mit.edu/linguistics/www/chomsky.home.html Pinker, S.  (1994).  The  language  instinct.  New York:  W.Morrow.

Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.

Refracted ray

According  to  Chomsky,  humans  are  born  with the LAD, but other species are not. Nonhuman primates and other species do not spontaneously learn human languages. Furthermore, attempts to teach nonhuman species language have yielded mixed results. Chimpanzees and gorillas have learned to use signed languages, such as American Sign Language (ASL). Washoe the chimpanzee and Koko the gorilla have each learned hundreds of signs and can use them to refer to concrete objects and concepts, such as hungry. However, neither has been able to master the intricacies involved in construction of grammatically correct sentences.

References: Chomsky, (1959). A review of B. F. Skinner’s Verbal behavior. Language, 35, 26–58. Chomsky,  (1986).  Knowledge  of  language:  Its  nature, origin, and use. New York: Praeger. Lenneberg,  (1967).  Biological  foundations  of  language. New York: Wiley. Noam Chomsky  home  page,  http://web.mit.edu/linguistics/www/chomsky.home.html Pinker, S.  (1994).  The  language  instinct.  New York:  W.Morrow.

What is refractive index

Now we have three incident rays whose refractive behavior is easily predicted. These three rays lead to our three rules of refraction for converging and diverging lenses. These three rules are summarized below.

Refractionexamples

Chomsky’s view of the LAD is consistent with there being specific structures in the brain involved in language learning and language processing. Such brain structures are presumably present in human brains, but absent in nonhuman brains. No specific claim was made regarding the specific location of the LAD in the brain. Although there have been locations in the brain identified as language processing areas, such as Broca’s area and Wernicke’s area, a location corresponding to the LAD has not been found.

These two "rules" will greatly simplify the task of determining the image location for objects placed in front of converging lenses. This topic will be discussed in the next part of Lesson 5. For now, internalize the meaning of the rules and be prepared to use them. As the rules are applied in the construction of ray diagrams, do not forget the fact that Snells' Law of refraction of light holds for each of these rays. It just so happens that geometrically, when Snell's Law is applied for rays that strike the lens in the manner described above, they will refract in close approximation with these two rules. The tendency of incident light rays to follow these rules is increased for lenses that are thin. For such thin lenses, the path of the light through the lens itself contributes very little to the overall change in the direction of the light rays. We will use this so-called thin-lens approximation in this unit. Furthermore, to simplify the construction of ray diagrams, we will avoid refracting each light ray twice - upon entering and emerging from the lens. Instead, we will continue the incident ray to the vertical axis of the lens and refract the light at that point. For thin lenses, this simplification will produce the same result as if we were refracting the light twice.

Chomsky, (1959). A review of B. F. Skinner’s Verbal behavior. Language, 35, 26–58. Chomsky,  (1986).  Knowledge  of  language:  Its  nature, origin, and use. New York: Praeger. Lenneberg,  (1967).  Biological  foundations  of  language. New York: Wiley. Noam Chomsky  home  page,  http://web.mit.edu/linguistics/www/chomsky.home.html Pinker, S.  (1994).  The  language  instinct.  New York:  W.Morrow.

5 applications ofrefractionof light

The above diagram shows the behavior of two incident rays approaching parallel to the principal axis. Note that the two rays converge at a point; this point is known as the focal point of the lens. The first generalization that can be made for the refraction of light by a double convex lens is as follows:

Now suppose that the rays of light are traveling through the focal point on the way to the lens. These rays of light will refract when they enter the lens and refract when they leave the lens. As the light rays enter into the more dense lens material, they refract towards the normal; and as they exit into the less dense air, they refract away from the normal. These specific rays will exit the lens traveling parallel to the principal axis.

References: Chomsky, (1959). A review of B. F. Skinner’s Verbal behavior. Language, 35, 26–58. Chomsky,  (1986).  Knowledge  of  language:  Its  nature, origin, and use. New York: Praeger. Lenneberg,  (1967).  Biological  foundations  of  language. New York: Wiley. Noam Chomsky  home  page,  http://web.mit.edu/linguistics/www/chomsky.home.html Pinker, S.  (1994).  The  language  instinct.  New York:  W.Morrow.

Now let's investigate the refraction of light by double concave lens. Suppose that several rays of light approach the lens; and suppose that these rays of light are traveling parallel to the principal axis. Upon reaching the front face of the lens, each ray of light will refract towards the normal to the surface. At this boundary, the light ray is passing from air into a more dense medium (usually plastic or glass). Since the light ray is passing from a medium in which it travels relatively fast (less optically dense) into a medium in which it travels relatively slow (more optically dense), it will bend towards the normal line. This is the FST principle of refraction. This is shown for two incident rays on the diagram below. Once the light ray refracts across the boundary and enters the lens, it travels in a straight line until it reaches the back face of the lens. At this boundary, each ray of light will refract away from the normal to the surface. Since the light ray is passing from a medium in which it travels relatively slow (more optically dense) to a medium in which it travels fast (less optically dense), it will bend away from the normal line. This is the SFA principle of refraction. These principles of refraction are identical to what was observed for the double convex lens above.

Optical refractiontest

We have already learned that a lens is a carefully ground or molded piece of transparent material that refracts light rays in such a way as to form an image. Lenses serve to refract light at each boundary. As a ray of light enters a lens, it is refracted; and as the same ray of light exits the lens, it is refracted again. The net effect of the refraction of light at these two boundaries is that the light ray has changed directions. Because of the special geometric shape of a lens, the light rays are refracted such that they form images. Before we approach the topic of image formation, we will investigate the refractive ability of converging and diverging lenses.

Some  researchers  have  rejected  the  notion  that language acquisition is aided by innate knowledge. In 1957, the behaviorist B. F. Skinner published the book Verbal Behavior, in which he argued that all types of language behavior were learned after birth through the same learning processes that are used for all human learning. Some contemporary cognitive scientists, such as David Rumelhart and James McClelland, as well as others, view language learning as the result of general learning principles, rather than language-specific mechanisms. According to Chomsky, the primary challenge for this alternative approach to language learning is adequately explaining how children produce word forms and sentences that they do not experience in the environment and, thus, have no opportunity to learn.

Optical refractionpdf

Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point).

These three rules of refraction for converging and diverging lenses will be applied through the remainder of this lesson. The rules merely describe the behavior of three specific incident rays. While there is a multitude of light rays being captured and refracted by a lens, only two rays are needed in order to determine the image location. So as we proceed with this lesson, pick your favorite two rules (usually, the ones that are easiest to remember) and apply them to the construction of ray diagrams and the determination of the image location and characteristics.

Now suppose that the rays of light are traveling towards the focal point on the way to the lens. Because of the negative focal length for double concave lenses, the light rays will head towards the focal point on the opposite side of the lens. These rays will actually reach the lens before they reach the focal point. These rays of light will refract when they enter the lens and refract when they leave the lens. As the light rays enter into the more dense lens material, they refract towards the normal; and as they exit into the less dense air, they refract away from the normal. These specific rays will exit the lens traveling parallel to the principal axis.

Chomsky’s claim that knowledge of language is innate was supported by Eric Lenneberg’s critical period hypothesis. In 1967, Lenneberg published the book Biological Foundations of Language, in which he argued that humans are biologically capable of learning language only until puberty. After puberty, humans are biologically unable to master the intricacies of natural language. For many years, researchers in zoology had recognized the existence of critical periods of development for a range of nonhuman animal species, such as songbirds, ducklings, horses, dogs, and sheep. Evidence for the Lenneberg’s critical period hypothesis for human language was drawn from a variety of sources. Case studies of children raised without sufficient exposure to human language appeared to support the critical period hypothesis. Such individuals, such as Victor, the wild child, and Genie, had not been able to master the grammatical intricacies of sentence construction. Individuals born with severe hearing loss who were not exposed to a signed language until after puberty typically had not been able to achieve nativelike proficiency. Furthermore, there was ample anecdotal evidence that individuals who attempt to learn a second language after puberty rarely achieve a level of proficiency comparable to that of one who learns the language during childhood.

The above discussion focuses on the manner in which converging and diverging lenses refract incident rays that are traveling parallel to the principal axis or are traveling through (or towards) the focal point. But these are not the only two possible incident rays. There are a multitude of incident rays that strike the lens and refract in a variety of ways. Yet, there are three specific rays that behave in a very predictable manner. The third ray that we will investigate is the ray that passes through the precise center of the lens - through the point where the principal axis and the vertical axis intersect. This ray will refract as it enters and refract as it exits the lens, but the net effect of this dual refraction is that the path of the light ray is not changed. For a thin lens, the refracted ray is traveling in the same direction as the incident ray and is approximately in line with it. The behavior of this third incident ray is depicted in the diagram below.

The language acquisition device (LAD) was proposed by Noam Chomsky to explain how children, when exposed to any human language, are able to learn it within only a few years following birth. Chomsky argued that all humans are born with the knowledge of what makes a human language. Included in this innate knowledge must be details of important characteristics of all the world’s languages. The term universal grammar has been used to describe the knowledge contained in the LAD. The process of language development is envisioned as one in which the child discovers which grammar rules contained within universal grammar apply to the language that the child is learning.

The above diagram shows the behavior of two incident rays traveling towards the focal point on the way to the lens. Note that the two rays refract parallel to the principal axis. A second generalization for the refraction of light by a double concave lens can be added to the first generalization.

The above diagram shows the behavior of two incident rays approaching parallel to the principal axis of the double concave lens. Just like the double convex lens above, light bends towards the normal when entering and away from the normal when exiting the lens. Yet, because of the different shape of the double concave lens, these incident rays are not converged to a point upon refraction through the lens. Rather, these incident rays diverge upon refracting through the lens. For this reason, a double concave lens can never produce a real image. Double concave lenses produce images that are virtual. This will be discussed in more detail in the next part of Lesson 5. If the refracted rays are extended backwards behind the lens, an important observation is made. The extension of the refracted rays will intersect at a point. This point is known as the focal point. Notice that a diverging lens such as this double concave lens does not really focus the incident light rays that are parallel to the principal axis; rather, it diverges these light rays. For this reason, a diverging lens is said to have a negative focal length.