A lens with 50-cm focal length produces a real image the same size as the object. How far from t

step 1 In this particular case it is given that F equals 50 centimeter and magnification is 1 which is

A lens with 50-cm focal length produces a real image the...

Key Concepts

Focal Length

The focal length of a lens is the distance from the lens at which light rays that are initially parallel converge to a point (for a converging lens) or appear to diverge from (for a diverging lens). This property determines the strength of the lens and is essential in calculating the positions of the object and the image using the lens equation.

Object-Image Symmetry

When a lens produces an image that is the same size as the object, it implies that the object and image distances are equal. This symmetry is a specific condition derived from the properties of the lens and the magnification equation. Recognizing this symmetry can simplify calculations by reducing the number of variables and directly linking the focal length to the object or image distance.

Magnification

Magnification in lens systems is defined as the ratio of the image height to the object height, and is mathematically given by m = -di/do. This concept not only indicates how much larger or smaller the image will be relative to the object, but also informs about the orientation of the image. A magnification of +1 or -1 (in absolute value) implies that the image is the same size as the object, with the sign indicating whether the image is upright or inverted.

Thin Lens Equation

The thin lens equation, given as 1/f = 1/do + 1/di, is a fundamental relation in geometrical optics that connects the focal length of a lens with the object distance (do) and the image distance (di). This equation is used to determine where an image will be formed given the position of the object and the focal length, assuming the lens is thin enough that its thickness can be neglected.

Real Image Formation

Real images are created when light rays converge after passing through a lens, allowing the image to be projected onto a screen. In the context of the thin lens equation, a real image is typically associated with positive image distances. Real image formation is a key principle in understanding how lenses can produce images that can be observed and captured in devices such as cameras and projectors.

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