Question

Why do we give 2 negative signs for object distance in Lens maker's formula? (i) A negative sign is already there in the equation. (ii) The second negative sign is along with the substituted value of object distance. Why?

Answer 1

Hint: A lens is a transmissive optical device that uses refraction to focus or disperse a light beam. A simple lens is made up of a single transparent piece, whereas a compound lens is made up of several simple lenses (elements) that are usually aligned along a common axis.

Complete step by step solution:
Ground and polished or molded to the desired shape, lenses are made from materials such as glass or plastic. Unlike a prism, which refracts light without focusing, a lens can focus light to form an image. Microwave lenses, electron lenses, acoustic lenses, and explosive lenses are examples of devices that focus or disperse waves and radiation other than visible light in the same way.
Spherical lenses are made by gluing together two spherical transparent surfaces. Spherical lenses are divided into two types:
Concave lenses
Convex lenses
Concave lenses are lenses that are made by gluing two spherical surfaces together so that they are curved inward. Convex lenses are lenses that are made by joining two spherical surfaces that bulge outward.
With appropriate sign conventions, the lens formula can be used in any situation. This lens formula works for both concave and convex lenses. The image is a virtual image on the same side of the lens as the object if the equation shows a negative image distance. If the focal length in this equation is negative, the lens is a diverging lens rather than a converging lens.
The lens equation expresses the relationship between object distance $d_0$, the image distance $d_i$ , and the focal length f . The equation is stated as follows:
\[\dfrac{1}{f}=\dfrac{1}{{{d}_{o}}}+\dfrac{1}{{{d}_{i}}}\]
Using the lens equation to calculate the image distance yields: The image is virtual and on the same side of the lens as the object, as indicated by the negative sign. A lens with a negative focal length that causes a beam of parallel rays to diverge after refraction, as in a virtual image.

Note:
The degree of convergence or divergence of light rays falling on a lens is measured by its power. The degree of convergence or divergence is determined by the lens' focal length. Various imaging devices, such as telescopes, binoculars, and cameras, use lenses. They're also used in glasses as visual aids to correct vision problems like myopia and hypermetropia.