Mirror formula for concave mirror when real image is formed Let us take a concave mirror of aperture mirror of aperture XY where a light ray AC is travelling parallel to principle axis from object AB to mirror at C and reflect through focus F and pass through A'. Focal length of a plane mirror is infinite. Now from the above diagram, it is clear that according to the law of vertically opposite angles the opposite angles are equal. 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. It may be written as, where, v = Distance of image from pole of mirror u = Distance of object from pole of mirror and, f = Focal length of the mirror Your email address will not be published. It is represented by the symbol f. For mirrors of small aperture, f=R/2. The derivation of mirror formula is given below. Learn Reflection of Light by Plane Mirror here. c. Focal length which is represented as ‘f’. After refraction, the rays are parallel to each other, and therefore, no image is obtained. Derive mirror formula of a concave mirrors. A plane mirror can be considered as a spherical mirror of infinite radius of curvature. Students must understand each step of the mirror formula derivation to get a piece of in-depth knowledge about the topic. Stay tuned with BYJU’S and learn various other derivation of physics formulas. Focal length and radius of curvature of a concave mirror are positive whereas convex mirror negative. You can use the mirror formula also to get the focal length of a plane mirror, where the image distance = − object distance In a spherical mirror: The distance between the object and the pole of the mirror is called the object distance(u). Required fields are marked *. In diagram, PF is the focal length of the mirror. deduction for object at F and image at infinity?? 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. The mirror formula is applicable for both, plane mirrors and spherical mirrors (convex and concave mirrors). Focal Length of Concave Mirror Formula. parallel to the focal axis), it is reflected back by 180* parallel to the focal axis. The distance below the axis is negative whereas the distance above is positive. The mirror formula is written as: The following assumptions are taken in order to derive the mirror formula. This website really helped me a lot in my exams and I also learnt such new things which our teacher had never taught us! 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’. The mirror formula derivation is provided here so that students can understand the concept of the topic in a better way. Your email address will not be published. According to the convention, the negative sign indicates the distance measured in the direction opposite to the incident ray while the positive sign indicates the distance measured in the direction of the incident ray. From the calculations in the second example problem it can be concluded that if a 4.0-cm tall object is placed 8.3 cm from a concave mirror having a focal length of 15.2 cm, then the image will be magnified, upright, 8.8-cm tall and located 18.3 cm behind the mirror. The mirror formula is applicable both in spherical mirrors (concave mirrors and convex mirrors) and in plane mirrors. Let AB be an object lying beyond the focus of a concave mirror. Principal section. From the figure given above, it is obvious that the object AB is placed at a distance of U from P which is the pole of the mirror. How is mirror formula applicable in plane mirrors. Focal length. Focal length is half of radius of curvature and hence it is infinity. By obtaining the Real image of a distant object at its focus, the focal length of the concave mirror can be estimated as shown in the diagram. 0 0. kalyanr. The diagram given below will help learners to understand the mirror formula derivation more effectively. It is an equation relating object distance and image distance with focal length is known as a mirror equation. Mirror Formula for Convex Mirror when Real Image is formed. The distance between the pole and the principal focus of the mirror, is called the focal length of the mirror. It is also known as a mirror formula. As a demonstration of the effectiveness of the Mirror equation and Magnification equation, consider the following example problem and its solution. Example Problem #1 A 4.0-cm tall light bulb is placed a distance of 35.5 cm from a convex mirror having a focal length of -12.2 cm. Focal length and radius of curvature of a concave mirror are positive where as that of convex mirror negative. Image distance which is represented as ‘v’. So we can write: This was the derivation of mirror formula. Hence the focus is at infinity and the focal length is infinite . 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’. Focal length (f) and field of view (FOV) of a lens are inversely proportional. The mirror formula is applicable for both, plane mirrors and spherical mirrors (convex and concave mirrors). Infinite Because focal length is basically half the radius of curvature where radius of curvature refers to radius of the circle of which mirror is a part of. Lets see the above shown diagram, Focal Length – The space between the pole P of concave mirror and the focus F is the focal length of concave mirror. What is Mirror Equation? Test Your Understanding and Answer These Questions: 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, Rules for Obtaining Images by Spherical Mirrors. This can be shown as follows... when a ray of light falls on the mirror perpendicularly (i.e. Mirror Formula helps us to find: a. When the object is placed at F that is the focal point, there is no formation of an image as the refracted rays neither diverge nor converge at a point. For a standard rectilinear lens, FOV = 2 arctan x / 2f, where x is the diagonal of the film. The derivation of the mirror formula is one of the most common questions asked in various board examinations as well as competitive examinations. The mirror formula is applicable for both, plane mirrors and spherical mirrors (convex and concave mirrors). It can be said that these parallel rays will converge at infinity. 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’. Mirror Formula. Object distance which is represented as ‘u’. 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