Question

Assertion (A): The magnification of a convex mirror is always positive and less than unity.

Reason (R): The image formed in a convex mirror is always virtual, erect and diminished in nature.

Then, which of the following statements is correct?

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, and R is not the correct explanation of A.
• C. A is true but R is false.
• D. A is false but R is true.

Answer 1

The correct option is A Both A and R are true, and R is the correct explanation of A.

A convex mirror always forms a virtual, erect and diminished image, irrespective of where the object is placed.
Magnification of a spherical mirror is the ratio of the height of the image to the height of the object.
A virtual image is always erect or upright, i.e. it is in the same orientation as the object.
So, the object height and the image height in a convex mirror are always positive, as they are measured upwards from the principal axis.
$⟹$ Magnification of a convex mirror is positive.
Also, since the image is diminished, its size (height) is smaller than that of the object.
$⟹$ Image height $<$ Object height
So, magnification of a convex mirror is always less than 1.
The statements A and R are correct, and R is hence the correct explanation of A.