# state the mirror formula and its magnification

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November 29th, 2020

Assumptions made: The lens is thin. Two concave mirrors of different sizes are placed facing one another. Rearranging to isolate do gives $\frac{1}{d_{\text{o}}}=\frac{1}{f}-\frac{1}{d_{\text{i}}}\\$. Refer to the Problem-Solving Strategies for Lenses. Explain your responses. Ask your question. 1. ), Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the distance of the object from the mirror. (c) Find the radius of curvature of the convex mirror formed by the cornea. Step 1. The convex mirror shown in Figure 3 also has a focal point. To a good approximation for a concave or semi-spherical surface, the point where the parallel rays from the sun converge will be at the focal point, so R = 2f = 80.0 cm. The reflected rays seem to originate from behind the mirror, locating the virtual image. e. All the distances … Obviously, if you walk behind the mirror, you cannot see the image, since the rays do not go there. Can a case 1 image be larger than the object even though its magnification is always negative? Use the law of reflection to prove that the focal length of a mirror is half its radius of curvature. The instrument used is called a keratometer, or curve measurer. Step 2. ; The lens has a small aperture. The rays falling on the smaller mirror retrace their paths. A mirror formula can be defined as the formula which gives the relationship between the distance of object ‘u’, the distance of image ‘v’, and the focal length of the mirror ‘f’. 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. Figure 8. Provide a sketch. Examine the situation to determine that image formation by a mirror is involved. Figure 6. Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. It is otherwise identical. Thus a real image can be projected onto a screen placed at this location. The formula for calculating microscopic magnification is simply the ocular lens magnification times the objective lens magnification. Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature. Construct a problem in which you determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor. (b) What is the focal length of the mirror? Example of Mirror Equation. (a) +0.111; (b) −0.334 cm (behind “mirror”); (c) 0.752cm, 9. Numerical Methods In Lens (A) Lens Formula Definition: The equation relating the object distance (u), the image distance (v) and the focal length (f) of the lens is called the lens formula. (credit: Laura D’Alessandro, Flickr). By the end of this section, you will be able to: We only have to look as far as the nearest bathroom to find an example of an image formed by a mirror. But parabolic mirrors are much more expensive to make than spherical mirrors. Does its size depend upon your distance away from the mirror? Explain with ray diagrams the formation of an image using spherical mirrors. Object distance is the distance of the object from the pole of the mirror; denoted by the letter u. The solution is to use a mirror that is small compared with its radius of curvature, as shown in Figure 2b. Rays of light that strike the surface follow the law of reflection. Using the law of reflection and some simple trigonometry, it can be shown that the focal length is half the radius of curvature, or $f=\frac{R}{2}\\$, where R is the radius of curvature of a spherical mirror. For example, dental mirrors may produce a magnified image, just as makeup mirrors do. It is a case 3 image—one that is upright and smaller than the object, just as for diverging lenses. It is also seen to be smaller than the object. (credit: kjkolb, Wikimedia Commons). (a) Parallel rays reflected from a large spherical mirror do not all cross at a common point. The expression which gives t… A shopper standing 3.00 m from a convex security mirror sees his image with a magnification of 0.250. (The reverse of rays 1 and 3 in Figure 2. (a) Case 2 images for mirrors are formed when a converging mirror has an object closer to it than its focal length. Consider the situation shown in Figure 4, concave spherical mirror reflection, in which an object is placed farther from a concave (converging) mirror than its focal length. The Mirror formula explains how object distance (u) and image distance (v) are related to the focal length of a spherical mirror. For a mirror that is large compared with its radius of curvature, as in Figure 2a, we see that the reflected rays do not cross at the same point, and the mirror does not have a well-defined focal point. Magnification produced by a spherical mirror gives the relative extent to which the image of an Read more about Mirror Formula and Magnification[…] Usually, you want the rays to emerge parallel, and this is accomplished by having the filament at the focal point of the mirror. We will use the law of reflection to understand how mirrors form images, and we will find that mirror images are analogous to those formed by lenses. Your instructor may wish to guide you on the level of complexity to consider in the electrical components. Part 1 is related to the current topic. (This is the mirror equivalent of the thin lens approximation.) Per meter of pipe, what will be the amount of sunlight concentrated onto the pipe, assuming the insolation (incident solar radiation) is 0.900 k W/m. 1. Parallel rays of light reflected from a convex spherical mirror (small in size compared with its radius of curvature) seem to originate from a well-defined focal point at the focal distance f behind the mirror. If the fluid-carrying pipe has a 2.00-cm diameter, what will be the temperature increase of the fluid per meter of pipe over a period of one minute? How can you tell (by looking) whether an image formed by a single lens or mirror is real or virtual? Some telephoto cameras use a mirror rather than a lens. What is the main disadvantage of using such a mirror compared with a flat one? In fact, this is how makeup mirrors act as magnifiers. Ray 1 approaches parallel to the axis, ray 2 strikes the center of the mirror, and ray 3 approaches toward the focal point. Log in. 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. Using the law of reflection—the angle of reflection equals the angle of incidence—we can see that the image and object are the same distance from the mirror.