Rule and Formation of Image by a Concave Lens

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Concave Lens – Ray diagram, Images Formed – with Steps

We have already studied some rules for the formation of images by convex lenses. There are similar rules for constructing ray-diagrams for obtaining images with concave lenses. These are given below.

Rule 1. A ray of light which is parallel to the principal axis of a concave lens, appears to be coming from its focus after refraction through the lens. This is shown in Figure. Here we have a concave lens L and its principal axis is X’ Y’. A ray of light AD parallel to the principal axis enters the concave lens, gets refracted at point D and goes in the direction DX. To a person looking into the concave lens from the right side, the refracted ray of light DX appears to be coming from the focus F of concave lens situated on its left side (as shown by dotted line) (see Figure).

Rule 2. A ray of light passing through the optical centre of a concave lens goes straight after passing through the lens. This is shown in Figure. The ray of light AC is passing through the optical centre C of concave lens. This ray of light goes straight in the direction CY after passing through the concave lens. It does not bend at all. Please note that a ray of light along the principal axis of a conave lens also goes straight.

Rule 3. A ray of light going towards the focus of a concave lens, becomes parallel to its principal axis after refraction through the lens. This rule is just the reverse case of the first rule and it is shown in Figure. Here a ray of light AD (coming from the object) is going towards the focus F’of the concave lens. It enters the concave lens and gets refracted (or bends) at point D. After passing through the concave lens, it becomes parallel to the principal axis of the lens and goes in the direction DX (see Figure).

At any given time, we will use only two of the above three types of light rays to draw the ray-diagrams to find the position of image formed by a concave lens.

Please note that no matter where the object is placed in front of a concave lens, the concave lens always forms a virtual, erect and diminished image of the object. When the distance of an object from a concave lens is changed, then only the position and size of the image changes. There are two main positions of an object in the case of a concave lens from the point of view of position and size of image. The object can be :

1. anywhere between optical centre (C) and infinity, and
2. at infinity.

We will discuss both these cases one by one. Let us first describe the formation of image by a concave lens when the object is anywhere between optical centre (C) and infinity.

Formation of Image by a Concave Lens

In Figure, we have a concave lens with optical centre C. And F is the focus of this lens. The arrow AB pointing upwards represents the object. Now, we want to find out the position, nature and size of the image of this object which will be formed by the concave lens. The method used for obtaining the images with concave lenses is very similar to the one we have used in the case of convex lenses. This is as follows.

Starting from the upper point A of the object AB, we draw a line AD parallel to the principal axis. Now, according to the first rule of image formation, this parallel ray AD should appear to be coming from focus F after refraction. So, we join DF by a dotted line and produce FD upwards in the direction DX by a solid line. Now, DX is the first refracted ray which appears to be coming from focus F of the concave lens.

We have now to draw a second ray of light starting from the same point A and passing through the optical centre C. For this we join the points A and C by a line. Thus, the line AC represents a ray of light passing through the optical centre C of the lens. Now, according to the second rule of image formation, this ray should go straight. So, we extend the line AC further in the direction CY. Thus, CY is the second refracted ray.

The two refracted rays DX and CY are diverging rays and appear to intersect at point A on the left side of the lens, only when they are produced backwards. So, to an eye placed on the right side of the concave lens (as shown in Figure), the top of arrow appears to be at A’. Thus, A is the virtual image of the top point A of the object. To get the complete image of the object, we draw A’B’ perpendicular to the axis from point A. Thus, A’B’ is the image of the object AB. The image is virtual, erect and smaller than the object. It is situated between the optical centre and focus (in front of the concave lens). From the above discussion we conclude that: When an object is placed anywhere between optical centre (C) and infinity in front of a concave lens, the image formed is :

1. between optical centre (C) and focus (F),
2. virtual and erect, and
3. diminished (smaller than the object).

If we move the object more and more away from the optical centre of the concave lens, the image
becomes smaller and smaller in size and moves away from the lens towards its focus. And when the object is at infinity, the image is formed at the focus (see Figure 27 on page 232). From this discussion we conclude that : When an object is at infinity from a concave lens, the image formed is :

1. at focus (F),
2. virtual and erect, and
3. highly diminished (much smaller than the object).

And before we conclude this discussion, here is a summary of the images formed by a concave lens.

Summary of the Images Formed by a Concave Lens

How to Distinguish Between a Convex Lens and a Concave Lens Without Touching Them
We keep the lens close to the page of a book and see the image of the writing of the book through it. If the letters of the book appear enlarged, then it is a convex lens; and if the letters appear diminished, then it is a concave lens. This is due to the fact that when an object is within the focus of a convex lens, it produces an enlarged image. But a concave lens produces a diminished image for all positions of the object. So, in this case the object (the book) has been placed within focus of the lens.

Uses of Concave Lenses

1. Concave lenses are used in spectacles to correct the defect of vision called myopia (or short-sightedness).
2. Concave lens is used as eye-lens in Galilean telescope.
3. Concave lenses are used in combination with convex lenses to make high quality lens systems for optical instruments.
4. Concave lens is used in wide-angle spyhole in doors.