explain the three rules of ray diagram for refraction of light through lenses
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Refraction by Lenses
The Anatomy of a Lens
Refraction by Lenses
Image Formation Revisited
Converging Lenses - Ray Diagrams
Converging Lenses - Object-Image Relations
Diverging Lenses - Ray Diagrams
Diverging Lenses - Object-Image Relations
The Mathematics of Lenses
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.
How a Lens Refracts Light
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.
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:
Refraction Rule for a Converging Lens
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.
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.
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.
Refraction Rules for a Converging Lens
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.
Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
The Thin Lens Approximation
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.
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