For a convex mirror, the focal length (f) is positive. Given f = 15 cm and object distance (u) = -10 cm (object distance is negative), using the mirror formula 1/f = 1/v + 1/u, we find the image distance (v) ≈ 6 cm. The image is virtual (as v is positive), erect, and diminished, formed behind the mirror at approximately 6 cm from it.
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Introduction to Image Formation in Convex Mirrors
Basic Principles of Convex Mirrors: Convex mirrors are diverging mirrors, meaning they spread out light rays that reflect off them. This property affects how images are formed by these mirrors, typically resulting in virtual, erect, and diminished images.
Object Placement and Mirror Specifications: In this scenario, an object is placed 10 cm away from a convex mirror with a focal length of 15 cm. The goal is to determine the position and nature of the image formed by the mirror.
Applying the Mirror Formula
Calculating Image Position: The mirror formula 1/f = 1/v + 1/u is used to find the image distance v. Here, f is the focal length and u is the object distance. Given f = 15 cm and u = −10 cm (object distance is negative for mirrors), we can calculate v.
Determining Image Position
Finding the Image Distance: Substituting the given values into the mirror formula, we find that the image distance v is approximately 6 cm. This distance is positive, indicating that the image is formed behind the mirror.
Nature of the Image
Characteristics of the Formed Image: The positive value of v in the context of a convex mirror indicates that the image is virtual. Additionally, images formed by convex mirrors are always erect and diminished compared to the object.
Summary of Image Properties: Therefore, for an object placed 10 cm from a convex mirror with a focal length of 15 cm, the image is formed approximately 6 cm behind the mirror. The image is virtual, erect, and smaller than the object. This example highlights the unique image-forming properties of convex mirrors in optical applications.