#### Converging Lens and Diverging Lens, Physics tutorial

Images Formed by the Convex (Converging) lens:

In this section discussion is on the image formed by the convex (converging) lens. Here, we are going to look at how image of the object is formed by the convex lens for three different object position discussed below.

In using ray diagram to determine the position of the image of an object formed by a lens either (convex or concave), a set of rules, similar to rules that govern the reflection case, exist. These are as follows:

i) a ray parallel to the principal axis incident on one side of the lens is refracted to the far side of the lens through the far focus as shown in (a) Figure given below.

ii) A ray passing through the near focus on one side emerges parallel to the principal axis on other side as shown in (b) Figure given below.

iii) A ray incident along the optical centre of the lens goes through to the other side without any deviation as shown in (c) Figure given below.

i) Object Placed at Distance Greater than 2f:

The figure given above shows ray diagram for image formed by the convex lens of focal length f, in which object OP is placed at distance greater than 2f from lens. Ray PQ that is parallel to principal axis is refracted through the principal focus to give ray QR. Then ray PC that is directed towards optical center C of lens through the lens undeviated to give ray CR. Two refracted rays QR and CR intersect at R to form the image IR. Hence IR gives magnitude of the image and CI the image distance and OC is the object distance so the magnification M as earlier defined equal to

M = IR/OP = CI/OC = Image distance/Object distance

ii) Object Placed at the Position 2f:

The figure given above shows the ray diagram for image formed by the convex lens of focal length f when object distance is 2f. Two rays considered are similar to those in Object Placed at Distance Greater than 2f. It can be seen from above Figure that image formed is real, inverted, and of unit magnification. I.e., size of the image is same as that of object.

iii) Object is kept at Principal Focus:

The given figure shows ray diagram for the image formed by the convex lens when object is kept at focus which is at focal length f. Considering just two rays either discussed above, ray PQ parallel to principal axis is refracted through the far focus to give ray Qf. Conversely ray PC goes through the optical centre of the lens undeviated on the other side. Therefore, we have the set of parallel rays emerging on the other side of the lens. As parallel rays (lines) only converge infinity, it applies that image formed under this situation is at infinity. Therefore, image formed by the convex lens, when object is placed at principal focus, is at infinity.

iv) Object kept between f and the Lens:

The figure given above shows the ray diagram for image formed by convex lens when object distance is less than focal length of lens. Ray PQ is refracted to give ray Qf while ray PC, as usual, is undeflected.

As a result, emerging, (refracted rays) diverge and appear to come from point R consequently given rise to image IR. It can be seen that image IR is virtual, erect and magnified.

Images Formed by Concave Lens:

The given figure shows ray diagram for the image formed by the concave (diverging) lens. As can be seen from figure that the ray PQ, parallel to axis, diverges at the other side of lens after refraction to give ray QR, ray PC through optical center of the lens passes through to the other side of the lens without any deviation. Therefore, image is formed by the intersection of apparent source of the divergent ray (dotted line) and ray PC. These two rays intersect at R. Thus, IC gives image distance and IR gives magnitude of the image. As before magnification of the image can be stated as

M = IR/OP = IC/OC

It can be observed from that image formed is imaginary, it is erect and it is diminished. Also it has been found that irrespective of position of Object, the shape of image and kind of the image formed are always the same.

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