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Physics Topics are also essential for space exploration, allowing scientists to study phenomena such as gravitational waves and cosmic rays.
How do you Find the Position Size and Nature of an Image?
In all the following discussions the lenses we shall deal with are thin lenses with small aperture.
To find the position of the image of an extended object placed on the principal axis of a lens by geometrical method we should remember the following facts:
i) A ray falling on a convex lens in a direction parallel to the principal axis converges to the second principal focus after refraction by the lens and a ray falling on a concave lens in a direction parallel to the principal axis appears to diverge from the second principal focus after refraction by the lens.
ii) A ray passing through the first principal focus of a convex lens or proceeding to the first principal focus of a concave lens will emerge parallel to the principal axis after refraction through it.
iii) A ray passing through the optical centre of a convex or a concave lens emerges out from the lens undeviated and undisplaced with respect to the direction of incidence as the concern lens is a thin lens.
Using any two rays of the above mentioned three rays, the image of an object can be drawn. In the section 3.11, images have been drawn in different cases applying this method. These diagrams are called ray diagrams.
Position, Size and Nature of the Image for Different Positions of an Object
For any particular surrounding media (here, air), the position, size and nature of the image of an object formed by refraction in a lens depend on the position of the object with respect to the lens. How the position and nature of the image change when the object is brought from infinity up to a position close to the lens is shown below. For convenience of discussion we shall consider the object PQ to be placed perpendicular to the principal axis of the lens LL’. (f is taken as focal length of the lens).
In case of convex lens:
1. Object is placed at infinity: If the object is at infinity, the rays of light from a point on the object may be considered as parallel [Fig.], The beam of parallel rays inclined at a small angle with the principal axis of the convex lens converges at the point p on the second principal focal plane after refraction in the lens. So, the image is formed in the focal plane and it is real, inverted and infinitely diminished.
Use: The objective of a telescope is made by using this property of the convex lens.
2. Object is placed between infinity and 2 f: The object PQ is placed perpendicular to the principle axis of the convex lens LL’ and at a distance greater than 2f from the lens [Fig.].
A ray from P travelling parallel to the principal axis after refraction through the lens passes through the focus P. Another ray from P goes straight through the optical centre O. These two refracted rays meet at the point p which is the image of P. From p, pq is drawn perpendicular to the principal axis. Obviously, q is the image of the foot Q of the object. So, pq is the image of PQ.
Therefore, the image is formed between f and 2f on the side of the lens opposite to that of the object. The image is real, inverted and diminished in size with respect to the object.
Use: The camera works on this property of the convex lens.
3. Object is placed at 2f: The object PQ is placed perpendicular to the principal axis of the convex lens LL’ and is at a distance 2f from the lens [Fig.]. A ray from P travelling parallel to the principal axis after refraction through the lens passes through the focus F. Another ray from P goes straight through the optical centre O. These two refracted rays meet at the point p which is the image of P. From p, pq is drawn perpendicular to the principal axis. Obviously, q is the image of the foot Q of the object. So, pq is the image of PQ.
Therefore, the image is formed on the side of the lens opposite to that of the object at a distance 2f from the lens. The image is real, inverted and equal in size to the object.
Use: In terrestrial telescope this property of the convex lens is utilised to convert the inverted image into an erect image of the same size.
4. Object is placed between f and 2f: The object PQ is placed perpendicular to the principal axis of the convex lens LL’ and is placed between f and 2f [Fig.], A ray from P travelling parallel to the principal axis after refraction through the lens passes through the focus F. Another ray from P goes straight through the optical centre O. These two refracted rays meet at the point p which is the image of P. From p, pq is drawn perpendicular to the principal axis. Obviously, q is the image of the foot Q of the object. So, pq is the image of PQ.
Therefore, the image is formed on the side of the lens opposite to that of the object and at a distance greater than 2f. The image is real, inverted and magnified in size with respect to the object.
Use: The objective of a microscope is made by utilising this property of the convex lens.
5. Object is placed at f: The object PQ is placed perpendicular to the principal axis of the convex lens LL’ and is placed at focus f [Fig.], A ray from P travelling parallel to the principal axis after refraction through the lens passes through the focus F. Another ray from P moves straight through the optical centre O. These two refracted rays being parallel, the image of PQ is assumed to be formed at infinity.
Therefore, the image is formed at infinity on the side of the lens opposite to that of the object. The image is real, inverted and infinitely magnified.
Use: The convex lens is utilised in the above way in such instruments where production of parallel beam of rays is required. In spectrometer parallel rays are produced in this way.
6. Object is placed between f and lens: The object PQ is placed perpendicular to the principal axis of the convex lens LL’ and is placed between f and the lens [Fig.]. A ray from P travelling parallel to the principal axis after refraction through the lens passes through the focus F. Another ray from P moves straight through the optical centre O. These two refracted rays are divergent. So when the two rays are produced backward they meet at p which is the virtual image of P. From p, pq is drawn perpendicular to the principal axis. So, pq is the image of PQ.
Therefore, the image is formed on the same side of the lens as the object is situated. The image is virtual, erect and magnified.
Use: Magnifying glass, eye pieces of microscope and telescope are made utilising this principle of the convex lens.
In case Of concave lens: The object PQ is placed per-pendicular to the principal axis of the concave lens LL’ [Fig.]. A ray from P travelling parallel to the principal axis after refraction through the lens appears to diverge from the focus F. Another ray from P moves straight through the optical centre O. The two refracted rays being divergent, when produced backwards, virtually meet at p. The point p from where the emergent rays appear to diverge after refraction through the lens is the image of P. From p, pq is drawn perpendicular to the principal axis. So, pq is the image of PQ.
Therefore, the image is formed on the same side of the lens as the object is situated. The image is virtual, erect and diminished in size with respect to the object.
The image moves from F to the lens and increases in size as the object is brought from infinity up to the lens. But the size of the image will always be less than the object.
Inference: The following inferences can be drawn from the above discussions.
- The virtual image is formed on the same side of the lens as the object but the real image is formed on the side of the lens opposite to that of the object.
- Virtual image is always erect and real image is always inverted.
If half of a lens is painted black, the brightness of the image produced by the lens reduces to half as image will be produced due to refraction through half portion of the lens. However, the size of the image remains the same, because every half part of a lens forms a complete image of an object.
Method of Identifying Lenses: we know that if an object is placed very near to a convex lens i.e., within the focal length, then a virtual, erect and magnified image is formed. On the other hand, when an object is placed very near to a concave lens a virtual, erect and diminished image is formed. So, to identify a lens easily we should hold a finger in front of the lens and look at it from the other side of the lens. If the image is erect and magnified with respect to the object the lens is convex. But if the image is erect but diminished in size, the lens is concave.