Question

Find out the correct option from the following.
(a) The magnification is positive for all virtual images and is negative for all real images.
(b) The magnification of concave lens and convex mirror is always positive whereas the magnification of convex lens and concave mirror can be positive or negative depending on the position of the object before the lens.
A. Only (a) is true.
B. Only (b) is true.
C. Both (a) and (b) are true.
D. Both (a) and (b) are false.

Answer 1

The ratio of the size of the image to the size of the object is called magnification. You need to consider the sign convention while considering distances and sizes. Height is taken as positive if it is above the principal axis and it is taken as negative when it is below the principal axis. Apply the sign convention for virtual and real images and find out the sigh of magnification for each case.

Complete step-by-step answer:
The magnification is the factor by which an image appears larger or smaller compared to the size of an object. It is the ratio of the height of the image to the height of the object. Thus, it can be given as $M=\dfrac{{{h}'}}{h}$
Where h is the height of the object and ${h}'$ is the height of the image.
It can also be written in terms of the object distance and the image distance,
$M=-\dfrac{v}{u}$

According to the sign conventions, all the distances above the principal axis are taken as positive and all the distances below the principal axis are taken as negative.
Thus, the height of the object is taken as positive. The real image is always formed as inverted, therefore, for real image height is taken as negative. The virtual image is always formed as upright, therefore, for virtual image height is taken as positive. If we use this sign convention, we will get positive magnification for all virtual images and negative magnification for all real images.

The concave lens and the convex mirror always produce a virtual image, therefore, their magnification is always positive whereas the convex lens and the concave mirror can produce real as well as the virtual image depending upon the object position, therefore, their magnification can be positive or negative.

Answer- C. Both a and b are true.

Note: Convex mirrors always produce a diminished and erect image, therefore they are used as rare mirrors in vehicles. Note that the option (a) is true only for a single optical device. For a combined system such as a compound microscope, a virtual and inverted image may be formed.