Figure 5. Parabolic trough collectors are used to generate electricity in southern California. We are considering only one meter of pipe here, and ignoring heat losses along the pipe. What happens if an object is closer to a concave mirror than its focal length? In fact, this is how makeup mirrors act as magnifiers. Figure 6a uses ray tracing to locate the image of an object placed close to a concave mirror. Rays from a common point on the object are reflected in such a manner that they appear to be coming from behind the mirror, meaning that the image is virtual and cannot be projected.
As with a magnifying glass, the image is upright and larger than the object. This is a case 2 image for mirrors and is exactly analogous to that for lenses. Figure 6. Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 approaches the mirror as if it came from the focal point. All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be larger than the object.
A convex mirror is a diverging mirror f is negative and forms only one type of image. It is a case 3 image—one that is upright and smaller than the object, just as for diverging lenses. Figure 7a uses ray tracing to illustrate the location and size of the case 3 image for mirrors.
Since the image is behind the mirror, it cannot be projected and is thus a virtual image. It is also seen to be smaller than the object. Figure 7. Case 3 images for mirrors are formed by any convex mirror. Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 approaches toward the focal point.
All three rays appear to originate from the same point after being reflected, locating the upright virtual image behind the mirror and showing it to be smaller than the object. Because the image is smaller, a larger area is imaged compared to what would be observed for a flat mirror and hence security is improved.
A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea. If the light source is If we can find the focal length of the convex mirror formed by the cornea, we can find its radius of curvature the radius of curvature is twice the focal length of a spherical mirror.
We first solve for the image distance d i , and then for f. Although the focal length f of a convex mirror is defined to be negative, we take the absolute value to give us a positive value for R. The radius of curvature found here is reasonable for a cornea. The distance from cornea to retina in an adult eye is about 2. In practice, many corneas are not spherical, complicating the job of fitting contact lenses.
Note that the image distance here is negative, consistent with the fact that the image is behind the mirror, where it cannot be projected.
The three types of images formed by mirrors cases 1, 2, and 3 are exactly analogous to those formed by lenses, as summarized in the table at the end of Image Formation by Lenses. It is easiest to concentrate on only three types of images—then remember that concave mirrors act like convex lenses, whereas convex mirrors act like concave lenses.
Find a flashlight and identify the curved mirror used in it. Find another flashlight and shine the first flashlight onto the second one, which is turned off. Estimate the focal length of the mirror. You might try shining a flashlight on the curved mirror behind the headlight of a car, keeping the headlight switched off, and determine its focal length. Step 2. Refer to the Problem-Solving Strategies for Lenses.
The same strategies are valid for mirrors as for lenses with one qualification—use the ray tracing rules for mirrors listed earlier in this section. Figure 8. Skip to main content. Geometric Optics. Search for:. Image Formation by Mirrors Learning Objectives By the end of this section, you will be able to: Illustrate image formation in a flat mirror. Explain with ray diagrams the formation of an image using spherical mirrors. Determine focal length and magnification given radius of curvature, distance of object and image.
Example 1. A Concave Reflector Electric room heaters use a concave mirror to reflect infrared IR radiation from hot coils. Example 2. Solar Electric Generating System One of the solar technologies used today for generating electricity is a device called a parabolic trough or concentrating collector that concentrates the sunlight onto a blackened pipe that contains a fluid.
If we wish to place the fluid-carrying pipe Per meter of pipe, what will be the amount of sunlight concentrated onto the pipe, assuming the insolation incident solar radiation is 0. If the fluid-carrying pipe has a 2. Assume all the solar radiation incident on the reflector is absorbed by the pipe, and that the fluid is mineral oil. Strategy To solve an Integrated Concept Problem we must first identify the physical principles involved.
Example 3. Image in a Convex Mirror A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. An incident ray which strikes the mirror at its vertex is reflected such that its angle of incidence with respect to the principal axis is equal to its angle of reflection. The validity of these rules in the paraxial approximation is, again, fairly self-evident. In the example shown in Fig.
It can be seen that the image is virtual, upright, and diminished. Figure Image formation by a convex mirror. As is easily demonstrated, application of the analytical method to image formation by convex mirrors again yields Eq. So if the object is positioned above the principal axis, then the image is positioned below the principal axis.
The object is on the convex side of the mirror so the image is located on the other side of the mirror and is upright. When the object is located betwee C and F, the image is located beyond C and is inverted.
So if the object is positioned below the principal axis, then the image is positioned above the principal axis. The object is located in front of F for a concave mirror, so the image is upright, virtual and on the opposite side of the mirror. So if the object is positioned below the principal axis, the image is positioned below the principal axis. Virtual images are always formed by convex mirrors and are formed by concave mirrors when the object is placed in front of F. Concave mirrors will do this when the object is at C or when the object is right on the mirror surface.
Plane mirrors and convex mirrors will always produce an upright image. A concave mirror will only produce an upright image if the object is located in front of the focal point. Plane mirrors and convex mirrors only produce virtual images. Only a concave mirror is capable of producing a real image and this only occurs if the object is located a distance greater than a focal length from the mirror's surface.
The image of an object is found to be upright and reduced in size. What type of mirror is used to produce such an image? Only a convex mirror could produce such an image. The upright images produced by concave mirrors when object is in front of F are magnified images.
And the upright images produced by plane mirrors have the same size as the object. Physics Tutorial. My Cart Subscription Selection.
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