Mathematically, a plane mirror can be considered to be the limit of either a concave or a convex spherical curved mirror as the radius, and therefore the focal length becomes infinity. The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). Applying this to triangles \(PAB\) and \(QAB\) in Figure \(\PageIndex{1}\) and using basic geometry shows that they are congruent triangles. Watch the recordings here on Youtube! Now OP 2 = OD 2 – DP 2, and. Later in this chapter, we discuss real images; a real image can be projected onto a screen because the rays physically go through the image. We verify this formula in this experiment. The difference is that a virtual image cannot be projected onto a screen, whereas a real image can. c. Focal length which is represented as ‘f’. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Watch this video to understand the significance of the mirror formula which is also applicable to the plane mirror. Images 1 and 2 result from rays that reflect from only a single mirror, but image 1,2 is formed by rays that reflect from both mirrors. The number of images formed by two adjacent plane mirrors depends on the angle between the mirror. [ "article:topic", "Magnification", "authorname:openstax", "plane mirror", "image distance", "object distance", "real image", "virtual image", "license:ccby", "showtoc:no", "program:openstax" ], 2.1: Prelude to Geometric Optics and Image Formation, Creative Commons Attribution License (by 4.0). However, in front of the mirror, the rays behave exactly as if they come from behind the mirror, so that is where the virtual image is located. Further Reading. PI 2 = DI 2 – DP 2. [4], Learn how and when to remove this template message, https://openstax.org/books/university-physics-volume-3/pages/2-2-spherical-mirrors, https://en.wikipedia.org/w/index.php?title=Plane_mirror&oldid=990988313, Articles needing additional references from June 2017, All articles needing additional references, Articles with unsourced statements from June 2017, Creative Commons Attribution-ShareAlike License, This page was last edited on 27 November 2020, at 17:40. So this mirror, the way it's shaped right here, based on how we're looking at it, is a concave mirror. If the reflected rays are extended backward behind the mirror (see dashed lines), they seem to originate from point \(Q\). For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. It may be written as, where, v = Distance of image from pole of mirror u = Distance of object from pole of mirror You may have noticed that image 3 is smaller than the object, whereas images 1 and 2 are the same size as the object. This means that the distance \(PB\) from the object to the mirror is the same as the distance \(BQ\) from the mirror to the image. The ratio of the image height with respect to the object height is called magnification. Note that we use the law of reflection to construct the reflected rays. For a plane mirror, the image will be the same size as the object and will be the same distance behind the mirror as the object is in front of the mirror. If we repeat this process for point \(P′P′\), we obtain its image at point \(Q′\). [math]\Rightarrow \qquad[/math] The angle of deviation for a plane mirror is [math]2(90^o-\theta) = 180^o-2\theta. The radius of curvature of a convex mirror used for rearview on a car is 4.00 m. If the location of the bus is 6 meters from this mirror, find the position of the image formed. Thus, the fronts and backs of images 1 and 2 are both inverted with respect to the object, and the front and back of image 3 is inverted with respect to image 2, which is the object for image 3. For plane mirror the usual mirror formula can be used usual mirror formula involves object distance u image distance v and f -the focal length which is equal to R/2 where R is the radius of curvature. [citation needed] The focal length of a plane mirror is infinity;[4] its optical power is zero. To understand how this happens, consider Figure \(\PageIndex{1}\). uv (cm 2) Slope=f (u+v) cm. The image formed by a plane mirror is always virtual (meaning that the light rays do not actually come from the image), upright, and of the same shape and size as the object it is reflecting. Actually, the image formed in the mirror is a perverted image (Perversion), there is a misconception among people about having confused with perverted and laterally-inverted image. Notice that each reflection reverses front and back, just like pulling a right-hand glove inside out produces a left-hand glove (this is why a reflection of your right hand is a left hand). It may be written as, where, v = Distance of image from pole of mirror. You should convince yourself by using basic geometry that the image height (the distance from \(Q\) to \(Q′\)) is the same as the object height (the distance from \(P\) to \(P′\)). Stay tuned with BYJU’S to learn about the application of the different types of mirrors, spherical mirrors, lenses, etc. The formula to find the number of images (n) formed between two plane mirrors inclined at angle, between them is as follows: Substituting the different values of angles between two inclined mirrors we can tabulate the answer as follows: Angle between the two mirrors () … To find image 1,2, you have to look behind the corner of the two mirrors. and, f = Focal length of the mirror. For light rays striking a plane mirror, the angle of reflection equals the angle of incidence. A straight line drawn from part of an object to the corresponding part of its image makes a right angle with, and is bisected by, the surface of the plane mirror. A plane mirror is made using some highly reflecting and polished surface such as a silver or aluminium surface in a process called silvering. Inserting this into Equation 2.3.1 for the radius R, we get. Images in a plane mirror are the same size as the object, are located behind the mirror, and are oriented in the same direction as the object (i.e., “upright”). Mirrors made from liquid also exist, as the elements gallium and mercury are both highly reflective in their liquid state. It means if you raise your left hand it would appear in the plane mirror that you have raised your right hand. In other words, in the small-angle approximation, the focal length f of a concave spherical mirror is half of its radius of curvature, R: f = R 2. Although one needs to be careful about the values, one puts for u,v and f with appropriate sign according to the si… This means that the distance PB from the object to the mirror is the same as the distance BQ from the mirror to the image. This is where the image of point \(P\) is located. And with the sign conventions we just discussed and the signs I'm using in this formula, concave mirrors always have a positive focal length. The law of reflection tells us that the angle of incidence is the same as the angle of reflection. [6] After silvering, a thin layer of red lead oxide is applied at the back of the mirror. A mirror formula may be defined as the formula which gives the relationship between the distance of image v, distance of object u, and the focal length of a mirror. A plane mirror is a mirror with a flat reflective surface. We have to see the rays coming from the object to see it. Have questions or comments? A plane mirror is a mirror with a flat (planar) reflective surface. Example of Mirror Equation. The object distance (denoted \(d_o\)) is the distance from the mirror to the object (or, more generally, from the center of the optical element that creates its image). If we measure distances from the mirror, then the object and image are in opposite directions, so for a plane mirror, the object and image distances should have the opposite signs: \[d_o=−d_i.\]