Question

Assertion: Magnification of a convex mirror is always positive, but that of a concave mirror may be both positive and negative.
Reason: It depends on the sign convention chosen.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but reason is incorrect.
D. Both Assertion and Reason are incorrect.

Answer 1

Hint: The magnification is the ratio of the image height to the object height. The virtual image always forms above the principal axis and the real image always forms below the principle axis. The magnification of the virtual image is always positive and the magnification of the real image is always negative.

Complete answer:
Let’s define the magnification of the mirror. It is the apparent size of an image formed by the mirror with respect to the size of an object. We know that the magnification is the ratio of the image height to the object height. Therefore, we can express the magnification as,
\[m = \dfrac{{{h_i}}}{{{h_o}}}\]
Here, \[{h_i}\] is the image height and \[{h_o}\] is the object height.

We know that according to the sign conventions, the object is always placed above the principle axis. Therefore, the object height is always positive. The image height may be positive or negative depending on the type of image formed. We know that the virtual image always forms above the principal axis and the real image always forms below the principle axis. Therefore, according to sign conventions, the height of the image if it is formed below the principle axis should be taken as negative.

Now, let’s discuss the type of image formed by concave mirror and convex mirror. We know that the convex mirrors always produce virtual, diminished and upright images while the concave mirror may produce both real and virtual images depending on the position of the object placed on the principal axis. As we have discussed in the above paragraph, the magnification of the virtual image is always positive, that is the magnification of a convex mirror is always positive and since the concave mirror forms both types of images, the magnification of the concave mirror can be both positive and negative.

According to the sign conventions, the distances along the positive y-axis above the principal axis are taken as positive while distances along the negative y-axis are taken as negative. Now, if we chose distance below the principle axis as positive and distance above the principle axis as negative, the magnification will still be the same because it is the ratio of image height to object height. For the convex mirror, both the object and image are above the principle axis and negative according to our chosen sign convention. Therefore, the ratio of their respective heights is positive. We can show the same for the concave mirror. Therefore, irrespective of the sign convention chosen, the magnification of the convex mirror is always positive, but that of a concave mirror may be both positive and negative.

So, the correct answer is option C.

Note: To answer such types of questions on mirrors and lenses, the things that should be on your fingertips are the sign conventions, formula for magnification and mirror equation. If you cannot remember the type of images formed by concave mirror and convex mirror, you can recall the structure of the mirrors and draw the ray diagrams. The real image forms when the refracted or reflected rays converge at a certain point. The virtual image forms by back tracing the refracted rays.