To find the image position, size, and nature for a converging lens, we use the lens formula 1/f = 1/v − 1/u and the magnification formula m = v/u = hi/ho. Given f = 10 cm and u = −25 cm (object distance is negative), solving the lens formula gives v ≈ 16.67 cm (positive, so the image is real and on the opposite side of the lens). The magnification m ≈ −0.67, indicating the image is inverted and smaller (about 3.35 cm in length).
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Introduction to Image Formation by Converging Lenses
Basic Principles of Lens Optics: Converging lenses, or convex lenses, are capable of bending light rays to meet at a point. The nature of the image formed by these lenses depends on the object’s distance from the lens, the lens’s focal length, and the lens’s optical properties.
Object and Lens Specifications: In this scenario, an object 5 cm in length is placed 25 cm away from a converging lens with a focal length of 10 cm. The objective is to determine the position, size, and nature of the image formed by the lens.
Calculating Image Position
Using the Lens Formula: The lens 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. With f = 10 cm and
u = −25 cm (object distance is taken as negative), solving the formula gives v ≈ 16.67 cm.
Determining Image Size
Applying the Magnification Formula: The magnification formula m v/u = hi/ho relates the image height hi to the object height ho. With m ≈ −0.67 (from v ≈ 16.67 cm and u = −25 cm), the image height is found to be approximately 3.35 cm, smaller than the object.
Nature of the Image
Real and Inverted: The positive value of v indicates that the image is real and formed on the opposite side of the lens. The negative magnification indicates that the image is inverted relative to the object.
Summary of Image Characteristics: Therefore, the image formed by the converging lens is located approximately 16.67 cm from the lens, is about 3.35 cm in length, and is real and inverted. This example illustrates the fundamental principles of image formation in convex lenses and their practical applications in optics.