Linear Magnification – The ratio of the height or size of the image to that of the object is known as “Linear Magnification” or simply magnification and is denoted by the letter m.
Therefore, using Eq. 14. 11, we get.
Following are adopted rules about the sign conventions of the lens.
- All the distances are measured from the optical centre of the lens.
- The distance of the real objects and real images are taken as positive and those of virtual objects and virtual images are taken as negative.
- The focal length is taken as positive for convex lens and negative for concave lens.
Example 14.4: the focal length of a convex lens is 20 cm. where should an object be placed so as to get its real image magnified four times?
Solution: Two cases arise
- When image is real and (ii) when image is virtual
- For real image
In this case
F = 20 cm , p =?
Since the magnification of the object is four times, thus
- For virtual image
In this case
F = 20 cm , p =?
Since magnification of the object is four times, thus is case of virtual image
In this case object should be placed at a distance of 15 cm from the lens.
Example 14.5: An object is situated at a distance of 10 cm from a concave lens of focal length of 15 cm. calculate the position, nature and magnification of the image.
Solution: Hence, object is real, therefore
P = + 10 cm
Focal length of a concave lens is taken negative, therefore,
Thus the image is 6 cm from the lens on the same side of the object. It is virtual and erect.
(Ignore the negative sign)
The size of the image is 0.6 times of the object.