How can I draw a ray and lens diagram?

Question

How do I draw a ray and lens diagram using a 1:5 or smaller ratio showing how to use 2 lenses(focal lengths 10cm and 20cm) to get a magnification of 10 times?

Answer 1

To draw these ray diagrams, we will have to recall the three "rules" of refraction for a double convex 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.
An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/refrn/u14l5da.html - go here for a picture to help

The method of drawing ray diagrams for double convex lens is described below. The description is applied to the task of drawing a ray diagram for an object located beyond the 2F point of a double convex lens.

Pick a point on the top of the object and draw three incident rays traveling towards the lens.
Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the lens. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel. Draw the third incident ray such that it travels directly to the exact center of the lens.






Once these incident rays strike the lens, refract them according to the three rules of refraction for converging lenses.
The ray that passes through the focal point on the way to the lens will refract and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray which traveled parallel to the principal axis on the way to the lens will refract and travel through the focal point. And the ray which traveled to the exact center of the lens will continue in the same direction. Place arrowheads upon the rays to indicate their direction of travel. Extend the rays past their point of intersection.




Mark the image of the top of the object.
The image point of the top of the object is the point where the two refracted rays intersect. All three rays should intersect at exactly the same point. This point is merely the point where all light from the top of the object would intersect upon refracting through the lens. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point. (See note below.)






Repeat the process for the bottom of the object.
The goal of a ray diagram is to determine the location, size, orientation, and type of image which is formed by the double convex lens. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the entire image can be filled in.




Some students have difficulty understanding how the entire image of an object can be deduced once a single point on the image has been determined. If the object is merely a vertical object (such as the arrow object used in the example below), then the process is easy. The image is merely a vertical line. In theory, it would be necessary to pick each point on the object and draw a separate ray diagram to determine the location of the image of that point. That would require a lot of ray diagrams as illustrated in the diagram below.


Fortunately, a shortcut exists. If the object is a vertical line, then the image is also a vertical line. For our purposes, we will only deal with the simpler situations in which the object is a vertical line which has its bottom located upon the principal axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis.

The ray diagram above illustrates that when the object is located at a position beyond the 2F point, the image will be located at a position between the 2F point and the focal point on the opposite side of the lens. Furthermore, the image will be inverted, reduced in size (smaller than the object), and real. This is the type of information which we wish to obtain from a ray diagram. These characteristics of the image will be discussed in more detail in the next section of Lesson 5.

Once the method of drawing ray diagrams is practiced a couple of times, it becomes as natural as breathing. Each diagram yields specific information about the image. The two diagrams below show how to determine image location, size, orientation and type for situations in which the object is located at the 2F point and when the object is located between the 2F point and the focal point.


It should be noted that the process of constructing a ray diagram is the same regardless of where the object is located. While the result of the ray diagram (image location, size, orientation, and type) is different, the same three rays are always drawn. The three rules of refraction are applied in order to determine the location where all refracted rays appear to diverge from (which for real images, is also the location where the refracted rays intersect).

In the three cases described above - the case of the object being located beyond 2F, the case of the object being located at 2F,and the case of the object being located between 2F and F - light rays are converging to a point after reflecting off the mirror. In such cases, a real image is formed. As discussed previously, a real image is formed whenever refracted light passes through the image location. While diverging lenses always produce virtual images, converging lenses are capable of producing both real and virtual images. As shown above, real images are produced when the object is located a distance greater than one focal length from the lens. A virtual image is formed if the object is located less than one focal length from the converging lens. To see why this is so, a ray diagram can be used.

A ray diagram for the case in which the object is located in front of the focal point is shown in the diagram at the right. Observe that in this case the light rays diverge after refracting through the lens. When refracted rays diverge, a virtual image is formed. As was done with plane mirrors, the image location can be found by tracing all light rays backwards until they intersect. For every observer, the refracted rays would seem to be diverging from this point; thus, the point of intersection of the extended refracted rays is the image point. Since light does not actually pass through this point, the image is referred to as a virtual image. Observe that when the object in located in front of the focal point, its image is an upright and enlarged image which is located on the object's side of the lens. In fact, one generalization which can be made about all virtual images produced by lenses (both converging and diverging) is that they are always upright and always located on the object's side of the lens.

Thus far we have seen via ray diagrams that a real image is produced when an object is located more than one focal length from a converging lens; and a virtual image is formed when an object is located less than one focal length from a converging lens (i.e., in front of F). But what happens when the object is located at F? That is, what type of image is formed when the object is located exactly one focal length from a converging lens? Of course a ray diagram is always one tool to help find the answer to such a question. However, when a ray diagram is used for this case, an immediate difficulty is encountered. The diagram below shows two incident rays and their corresponding refracted rays.


For the case of the object located at the focal point (F), the light rays neither converge nor diverge after refracting through the lens. As shown in the diagram above, the refracted rays are traveling parallel to each other. Subsequently, the light rays will not converge to form a real image; nor can they be extended backwards on the opposite side of the lens to intersect to form a virtual image. So how should the results of the ray diagram be interpreted? The answer: there is no image!! Surprisingly, when the object is located at the focal point, there is no location in space at which an observer can sight from which all the refracted rays appear to be diverging. An image cannot be found when the object is located at the focal point of a converging lens.



There are more diagrams on the site as well.

Answer 2

no focal point and focal lenght are different. The focal point is the point where light passes throught after going through the concave lens. Focal lenght on the other hand, is the distance between the optical centre(centre of the lens) and the focal point ...(it's pretty much like the optical plane , only this is actually on the x-axis)

Answer 3

A pencil?