Question

Assertion: Magnification of a convex mirror is always positive, but that of a concave mirror may be both positive or 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: Try and remember the types of images that convex and concave mirrors form in terms of their orientation with respect to their principal axis. In other words, in general, do they form upright images, or inverted images or both? Remember that the orientation of images may depend on the distance of the object from the centre of curvature.

Complete step-by-step answer:
Let us begin by defining magnification.
It is a process by which we can enlarge the apparent size but not the physical size of an object. This enlargement is quantified by the number “magnification”. When this number is less than one, it refers to a reduction in size and is called minification or de-magnification.

Now that we’ve established what magnification is, let us try and understand what convex and concave mirrors are. They both are curved mirrors.

A convex mirror is a curved mirror where the reflective surface bulges out towards the light source. It is also called a diverging mirror since they cannot be used to focus light.

A concave mirror, however, has the reflective surface that is curved inwards away from the light source. It is also called a converging mirror as it reflects light inward to one focal point.

Convex mirrors always form virtual, diminished and upright images. Concave mirrors form real and inverted images or virtual and erect images.

Now, the sign of the magnification is indicative of the orientation of the image. According to the New Cartesian Sign Convention, convex mirrors, which always form upright images have a positive magnification whereas concave mirrors that form both erect and inverted images may have positive or negative magnification respectively. However, one can use a different sign convention as well, but it should be well defined and the inferences should be consistent with the definition.

Thus, we can conclude that statements of both assertion and reason are correct, however, the reason is not a justification for the assertion.

So, the correct answer is “Option B”.

Note:
Do not get confused with the sign and the number for magnification. The sign indicates whether the image is upright or inverted whereas the number indicates if the image is diminished in size or magnified.

$ Magnification = \dfrac{apparent(image) size}{true(object) size}$
If it is > 1 it means that the image is magnified whereas if it is between 0 and 1 the image is minified.
Therefore, total magnification is given by

$Magnification_{resultant} = \pm Magnification$
According to our above chosen convention if it is “+” it means that the image is upright whereas if it is “-“ the image is inverted.