Question

Draw a ray diagram to show the formation of an image, an object placed in front of the lens at any position of your choice except infinity.

Answer 1

Here, we are required to draw a ray diagram for the formation of an image of an object placed in front of the lens. Here, we are not given the type of lens or the position of the object. Hence, we will consider any case for both – concave lens and convex lens. For the ray diagram, the image can be obtained by the intersection of two rays coming from the object.

Complete answer:
Let us consider a convex lens with centre of curvature $C_1$ and $C_2$ . For simplicity we will consider both the curvature of the lens equal as shown in the figure.

Now, we know that the centre of the lens is known as the optical centre and the horizontal axis passing through the optical centre is known as the principle axis. Both the centres of curvatures lie on the principle axis.

The points $f_1$ and $f_2$ shows the focal points for both curvatures, which are defined as the points where the light rays travelling parallel to principal axis meet after refraction from lens or the point from which the originated light rays become parallel to the principal axis after refraction from lens. Now, let us assume a line object of certain height present on the centre of curvature as shown in the figure,

Now, to obtain the image of the object we will consider two light rays emerging from the object. One ray will originate parallel to the principle axis, and as we know, it will pass through the second focal point after getting refracted through the lens.

The other ray originating from the object will pass through the first focal point, and we know that it will become parallel to the principle axis after refraction through the lens. The image will be formed at the intersection point of the two rays as shown in the figure below.

The above diagram shows the ray diagram for the object placed at the centre of curvature of the lens. From the above diagram, we can understand that the image of the object will be real, inverted and of the same size as the object.

Note: Here, we have considered the object to be at the centre of curvature. We can consider various other cases. For example,
-If the object is placed beyond the centre of curvature, the image will be real, inverted and diminished between the centre of curvature and focal point.
-If the object is placed between the centre of curvature and focal point, the image will be real, inverted and magnified beyond the centre of curvature.
-If the object is placed at the focal point, the image will be real, inverted and highly magnified at infinity.
-If the object is placed between the focal point and optical centre, the centre will be imaginary, erect and magnified on the same side of the lens.
-For a concave lens, the image will always be virtual as the rays diverge after refraction from the lens.