Is it possible to form a virtual image with a positive converging 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. When the object is located at a location beyond the 2F point, the image will always be located somewhere in between the 2F point and the focal point F on the other side of the lens.

Regardless of exactly where the object is located, the image will be located in this specified region. In this case, the image will be an inverted image.

That is to say, if the object is right side up, then the image is upside down. In this case, the image is reduced in size ; in other words, the image dimensions are smaller than the object dimensions. If the object is a six-foot tall person, then the image is less than six feet tall. Earlier in Unit 13, the term magnification was introduced; the magnification is the ratio of the height of the object to the height of the image.

In this case, the magnification is a number with an absolute value less than 1. Finally, the image is a real image. Light rays actually converge at the image location.

If a sheet of paper were placed at the image location, the actual replica or likeness of the object would appear projected upon the sheet of paper. When the object is located at the 2F point, the image will also be located at the 2F point on the other side of the lens. In this case, the image will be inverted i. The image dimensions are equal to the object dimensions. A six-foot tall person would have an image that is six feet tall; the absolute value of the magnification is exactly 1.

As such, the image of the object could be projected upon a sheet of paper. When the object is located in front of the 2F point, the image will be located beyond the 2F point on the other side of the lens.

Real images can be formed by concave, convex and plane mirrors. Convex converging lenses can form either real or virtual images cases 1 and 2, respectively , whereas concave diverging lenses can form only virtual images always case 3. Real images are always inverted, but they can be either larger or smaller than the object. A real image is an image that can be projected onto a screen. A virtual image appears to come from behind the lens. The virtual image is always erect.

The common example of virtual image is the image formed in the mirror when we stand in front of that mirror. A realimage is that image which is formed when the light rays coming from an object actually meet each other after reflection or refraction.

The concave lens will not produce real images. Real images are not formed by a concave lens since the rays passing through the concave lens diverges and will never meet. A concave lens is a lens that possesses at least one surface that curves inwards. It is a diverging lens, meaning that it spreads out light rays that have been refracted through it. A concave lens is thinner at its centre than at its edges, and is used to correct short-sightedness myopia.

A concave lens is the opposite of a convex lens. Here one or both of the lenses surfaces are curved inwards. That is, the centre of the lens is closer to the plane than the edge. A concave lens is used to correct short-sightedness myopia. A convex lens is thicker at the centre and thinner at the edges. A concave lens is thicker at the edges and thinner at the centre. Due to the converging rays, it is called a converging lens.

Real image is found when the rays of light converge at a point after reflection on a mirror or after refraction through a lens. The intersection of the two rays gives the position of the image.

A third ray could be drawn which passes through the focal point on the left side of the lens; after passing through the lens, it would travel parallel to the axis, and would intersect the other two rays at the point where those rays already intersect.

Note that the real image is inverted. The image happens to be larger than the object. That happens because the object is between f and 2f away from the lens; if the lens were farther away than 2f, the image would be closer to the lens than 2f, and would be smaller than the object.