Why does convex lens converge

The focal point is denoted by the letter F on the diagrams below. Note that each lens has two focal points - one on each side of the lens. Unlike mirrors, lenses can allow light to pass through either face, depending on where the incident rays are coming from. Subsequently, every lens has two possible focal points. The distance from the mirror to the focal point is known as the focal length abbreviated by f.

Technically, a lens does not have a center of curvature at least not one that has any importance to our discussion. However a lens does have an imaginary point that we refer to as the 2F point.

This is the point on the principal axis that is twice as far from the vertical axis as the focal point is. As we discuss the characteristics of images produced by converging and diverging lenses, these vocabulary terms will become increasingly important.

Remember that this page is here and refer to it as often as needed. Physics Tutorial. My Cart Subscription Selection. Student Extras. Why just read about it and when you could be interacting with it? Interact - that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Optics Bench Interactive. You can find this in the Physics Interactives section of our website.

The Optics Bench Interactive provides the learner an interactive enivronment for exploring the formation of images by lenses and mirrors. The more powerful the lens, the closer to the lens the rays will cross. The greater effect a lens has on light rays, the more powerful it is said to be. For example, a powerful converging lens will focus parallel light rays closer to itself and will have a smaller focal length than a weak lens.

The light will also focus into a smaller and more intense spot for a more powerful lens. The power P of a lens is defined to be the inverse of its focal length. The power of a lens P has the unit diopters D , provided that the focal length is given in meters. Note that this power optical power, actually is not the same as power in watts defined in the chapter Work, Energy, and Energy Resources. It is a concept related to the effect of optical devices on light.

Optometrists prescribe common spectacles and contact lenses in units of diopters. Suppose you take a magnifying glass out on a sunny day and you find that it concentrates sunlight to a small spot 8.

What are the focal length and power of the lens? The situation here is the same as those shown in Figure 1 and Figure 2. The magnifying glass is a convex or converging lens, focusing the nearly parallel rays of sunlight. Thus the focal length of the lens is the distance from the lens to the spot, and its power is the inverse of this distance in m.

The focal length of the lens is the distance from the center of the lens to the spot, given to be 8. To find the power of the lens, we must first convert the focal length to meters; then, we substitute this value into the equation for power. This gives. This is a relatively powerful lens. The power of a lens in diopters should not be confused with the familiar concept of power in watts. If you examine a prescription for eyeglasses, you will note lens powers given in diopters.

If you examine the label on a motor, you will note energy consumption rate given as a power in watts. Figure 3. Rays of light entering a diverging lens parallel to its axis are diverged, and all appear to originate at its focal point F. The dashed lines are not rays—they indicate the directions from which the rays appear to come. The focal length f of a diverging lens is negative. Figure 3 shows a concave lens and the effect it has on rays of light that enter it parallel to its axis the path taken by ray 2 in the Figure is the axis of the lens.

The concave lens is a diverging lens , because it causes the light rays to bend away diverge from its axis. In this case, the lens has been shaped so that all light rays entering it parallel to its axis appear to originate from the same point, F, defined to be the focal point of a diverging lens.

The distance from the center of the lens to the focal point is again called the focal length f of the lens. Note that the focal length and power of a diverging lens are defined to be negative.

For example, if the distance to F in Figure 3 is 5. An expanded view of the path of one ray through the lens is shown in the Figure to illustrate how the shape of the lens, together with the law of refraction, causes the ray to follow its particular path and be diverged. As noted in the initial discussion of the law of refraction in The Law of Refraction , the paths of light rays are exactly reversible. This means that the direction of the arrows could be reversed for all of the rays in Figure 1 and Figure 3.

For example, if a point light source is placed at the focal point of a convex lens, as shown in Figure 4, parallel light rays emerge from the other side. Figure 4. A small light source, like a light bulb filament, placed at the focal point of a convex lens, results in parallel rays of light emerging from the other side.

The paths are exactly the reverse of those shown in Figure 1. This technique is used in lighthouses and sometimes in traffic lights to produce a directional beam of light from a source that emits light in all directions. Figure 6. The light ray through the center of a thin lens is deflected by a negligible amount and is assumed to emerge parallel to its original path shown as a shaded line.

Ray tracing is the technique of determining or following tracing the paths that light rays take. For rays passing through matter, the law of refraction is used to trace the paths. Here we use ray tracing to help us understand the action of lenses in situations ranging from forming images on film to magnifying small print to correcting nearsightedness.

While ray tracing for complicated lenses, such as those found in sophisticated cameras, may require computer techniques, there is a set of simple rules for tracing rays through thin lenses. A thin lens is defined to be one whose thickness allows rays to refract, as illustrated in Figure 1, but does not allow properties such as dispersion and aberrations.

An ideal thin lens has two refracting surfaces but the lens is thin enough to assume that light rays bend only once. A thin symmetrical lens has two focal points, one on either side and both at the same distance from the lens.

See Figure 6. Another important characteristic of a thin lens is that light rays through its center are deflected by a negligible amount, as seen in Figure 5. Thin lenses have the same focal length on either side. A thin lens is defined to be one whose thickness allows rays to refract but does not allow properties such as dispersion and aberrations.

Look through your eyeglasses or those of a friend backward and forward and comment on whether they act like thin lenses. Using paper, pencil, and a straight edge, ray tracing can accurately describe the operation of a lens. The rules for ray tracing for thin lenses are based on the illustrations already discussed:. In some circumstances, a lens forms an obvious image, such as when a movie projector casts an image onto a screen. In other cases, the image is less obvious. Where, for example, is the image formed by eyeglasses?

We will use ray tracing for thin lenses to illustrate how they form images, and we will develop equations to describe the image formation quantitatively. Figure 7. Ray tracing is used to locate the image formed by a lens.

Rays originating from the same point on the object are traced—the three chosen rays each follow one of the rules for ray tracing, so that their paths are easy to determine. The image is located at the point where the rays cross. In this case, a real image—one that can be projected on a screen—is formed. Consider an object some distance away from a converging lens, as shown in Figure 7.

The Figure shows three rays from the top of the object that can be traced using the ray tracing rules given above. Rays leave this point going in many directions, but we concentrate on only a few with paths that are easy to trace.

The first ray is one that enters the lens parallel to its axis and passes through the focal point on the other side rule 1. The second ray passes through the center of the lens without changing direction rule 3. The third ray passes through the nearer focal point on its way into the lens and leaves the lens parallel to its axis rule 4. The three rays cross at the same point on the other side of the lens.

Rays from another point on the object, such as her belt buckle, will also cross at another common point, forming a complete image, as shown. Although three rays are traced in Figure 7, only two are necessary to locate the image.

It is best to trace rays for which there are simple ray tracing rules. Before applying ray tracing to other situations, let us consider the example shown in Figure 7 in more detail. The image formed in Figure 7 is a real image , meaning that it can be projected. That is, light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye, for example.

Figure 8 shows how such an image would be projected onto film by a camera lens. This Figure also shows how a real image is projected onto the retina by the lens of an eye. Note that the image is there whether it is projected onto a screen or not.

The image in which light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye is called a real image. Figure 8. Real images can be projected.

Several important distances appear in Figure 7. We define d o to be the object distance, the distance of an object from the center of a lens. Image distance d i is defined to be the distance of the image from the center of a lens.

The height of the object and height of the image are given the symbols h o and h i , respectively. Images that appear upright relative to the object have heights that are positive and those that are inverted have negative heights.

Using the rules of ray tracing and making a scale drawing with paper and pencil, like that in Figure 7, we can accurately describe the location and size of an image. But the real benefit of ray tracing is in visualizing how images are formed in a variety of situations.

To obtain numerical information, we use a pair of equations that can be derived from a geometric analysis of ray tracing for thin lenses. The thin lens equations are. The minus sign in the equation above will be discussed shortly.

We will explore many features of image formation in the following worked examples. A clear glass light bulb is placed 0. Use ray tracing to get an approximate location for the image. Then use the thin lens equations to calculate both the location of the image and its magnification. Verify that ray tracing and the thin lens equations produce consistent results. Figure 9. A light bulb placed 0.

Ray tracing predicts the image location and size. Since the object is placed farther away from a converging lens than the focal length of the lens, this situation is analogous to those illustrated in Figure 7 and Figure 8. Ray tracing to scale should produce similar results for d i. A convex lens is a converging lens. When parallel rays of light pass through a convex lens the refracted rays converge at one point called the principal focus.

The distance between the principal focus and the centre of the lens is called the focal length. The rays of light from the person are converged by the convex lens forming an image on the film or charged couple device in the case of a digital camera. The angle at which the light enters the lens depends on the distance of the object from the lens. If the object is close to the lens the light rays enter at a sharper angled. This results in the rays converging away from the lens.

As the lens can only bend the light to a certain agree the image needs to be focussed in order to form on the film. This is achieved by moving the lens away from the film. Similarly, if the object is away from the lens the rays enter at a wider angle.