Using the mirror formula 1/f = 1/v + 1/u for a concave mirror, with f = −18 cm (focal length is negative for concave mirrors) and u = −27 cm (object distance is negative), we find v ≈ −54 cm. The screen should be placed 54 cm in front of the mirror. The image is real, inverted, and magnified. Using the magnification formula, the image size is approximately 14 cm.
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Introduction to Image Formation by Concave Mirrors
Fundamentals of Concave Mirror Optics: Concave mirrors are converging mirrors that can form real, inverted images when the object is placed outside the focal length. The nature and size of the image depend on the object’s distance from the mirror and the mirror’s focal length.
Object and Mirror Specifications: In this scenario, an object of size 7.0 cm is placed 27 cm in front of a concave mirror with a focal length of 18 cm. The objective is to determine the appropriate distance for a screen to obtain a sharp focused image, along with the size and nature of the image.
Calculating the Image Position
Using the Mirror Formula: The mirror formula 1/f = 1/v + 1/u is used to find the image distance v. For a concave mirror, f is -18 cm and u is -27 cm (object distance is negative). Solving this gives v ≈ − 54 cm.
Determining Screen Placement
Screen Position for Focused Image: The negative value of v indicates that the image is formed on the same side as the object. Therefore, the screen should be placed 54 cm in front of the mirror to obtain a sharp, focused image.
Nature and Size of the Image
Characteristics of the Formed Image: The image formed will be real and inverted, as indicated by the negative image distance in the context of a concave mirror. Using the magnification formula m = v/u, the magnification is 2, meaning the image size will be twice the object size, approximately 14 cm.
Summary of Image Properties: Thus, for an object placed 27 cm in front of a concave mirror with an 18 cm focal length, a sharp focused image is formed 54 cm from the mirror. The image is real, inverted, and twice the size of the object, measuring about 14 cm in length. This demonstrates the predictable behaviour of image formation in concave mirrors.