Share with associates

When an object is placed in front of a mirror or a lens, an image may be formed (when object is placed at the focal point of convex lens or concave mirror no image is formed). Now whether the image will be real or virtual and its position depend upon distance of the object, type of the lens or mirror and also their geometric construct. Yet it is required to establish a sign convention in order to find a relation between object distance, image distance and focal distance. There are a few sign conventions in Optcis, such as: Cartesian convention, real positive convention etc. Here we will discuss the real positive convention. Acoording to this one:

(i) Every distance has to be measured from the pole of reflecting or refracting plane or the optical center of the lens.

(ii) All real distances are positive. Here ‘real’ means the distance ray of light has actually traveled.

(iii) All virtual distances are negative. Here ‘virtual’ means the distance ray of light hasn’t actually traveled, but it seems to have traveled.

According to the above mentioned convention, following conclusions can be drawn:

(i) In case of the image formed by converging of rays of light after reflection or refraction, AKA real image, the concerned distance is positive. For similar reasons, distance of virtual image is negative. Because in order to form this, rays of light didn’t converge after reflection or refraction, they diverged. So frankly, no image is formed in this case, but the way reflected or refracted rays enter our eyes, we perceive to see an image that looks fully or partially like the object. That’s why virtual image can’t be focused on a screen, real image can.

(ii) In case of convex lens and concave mirrors, rays of light parallel to the principal axis are converged at a point on the axis, that’s why the focal lengths of these two are positive. Otherwise happens for concave lens and convex mirror, that’s why the focal points as well as the focal lengths of these two are negative. For similar reasons, when refraction takes place from lighter to denser medium the radii of curvature of concave and convex planes are respectively negative and positive. On the other hand, when refraction takes place from denser to lighter medium the radii of curvature of concave and convex planes are respectively positive and negative.

(iii) If object is situated in the same side from where the rays of light have arrived at the mirror, lens or refractive plane, the distance (u) of such object is positive. It the object is situated on the other side, the distance of such object is considered negative and the object itself is considered virtual or unreal. For example, consider refraction in the following coaxial convex lenses.