The Mathematics of Lenses Previously in Lesson 5ray diagrams were constructed in order to determine the location, size, orientation, and type of image formed by double concave lenses i.
The Mathematics of Lenses One theme of the Reflection and Refraction units of The Physics Classroom Tutorial has been that we see an object because light from the object travels to our eyes as we sight along a line at the object. Similarly, we see an image Converging and diverging mirrors an object because light from the object reflects off a mirror or refracts through a transparent material and travel to our eyes as we sight at the image location of the object.
From these two basic premises, we have defined the image location as the location in space where light appears to diverge from.
Because light emanating from the object converges or appears to diverge from this location, a replica or likeness of the object is created at this location. For both reflection and refraction scenarios, ray diagrams have been a valuable tool for determining the path of light from the object to our eyes.
Applying the Three Rules of Refraction In this section of Lesson 5, we will investigate the method for drawing ray diagrams for objects placed at various locations in front of a double convex lens.
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 that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.
Earlier in this lesson, the following diagram illustrating the path of light from an object through a lens to an eye placed at various locations was shown. In this diagram, five incident rays are drawn along with their corresponding refracted rays.
Each ray intersects at the image location and then travels to the eye of an observer. Every observer would observe the same image location and every light ray would follow the Snell's Law of refraction. Yet only two of these rays would be needed to determine the image location since it only requires two rays to find the intersection point.
Of the five incident rays drawn, three of them correspond to the incident rays described by our three rules of refraction for converging lenses. We will use these three rays through the remainder of this lesson, merely because they are the easiest rays to draw.
Certainly two rays would be all that is necessary; yet the third ray will provide a check of the accuracy of our process. Step-by-Step Method for Drawing Ray Diagrams 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. Draw the third incident ray such that it travels directly to the exact center of the lens. Place arrowheads upon the rays to indicate their direction of travel.
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 that traveled parallel to the principal axis on the way to the lens will refract and travel through the focal point.
And the ray that traveled to the exact center of the lens will continue in the same direction. 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 three 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.
Repeat the process for the bottom of the object. One goal of a ray diagram is to determine the location, size, orientation, and type of image that 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.Mar 03, · Yea, that was my first thought, but then I kept forgetting if the "CONVE" rule was for mirrors or lenses. Convex lens = converging lens, but convex .
How can a plane mirror, concave mirror, convex mirror, converging lens and/or diverging lens be used to produce an image that has the same size as the object? See Answer Plane mirrors will always do this.
Concave mirrors will do this when the object is at C or when the object is right on the mirror surface. Geometric Optics Converging Lenses and Mirrors Physics Lab IV Objective a point.
For this reason, concave mirrors are also referred to as converging mirrors. Rays incident on a convex mirror diverge away from the mirror, and is therefore referred to as diverging mirror. Convex lenses converge the rays passing through them, and.
#7 MedPR, Mar 3,