Question

Given that I is the image of a point object O formed by a spherical mirror, which of the following statements is incorrect?
A. If O and I are on the same side of the principal axis, then they have to be on the opposite sides of the mirror.
B. If O and I are on the opposite sides of the principal axis, then they have to be on the same side of the mirror.
C. If O and I are on the opposite sides of the principal axis, then they have to be on the opposite side of the mirror.
D. If O is on the principal axis, then Image has to lie on the principal axis only.

Answer 1

Hint: In the case of mirrors, the real image and the object are on the same side of the mirror, and they are on the opposite sides of the principal axis. The virtual image and the object are on the opposite sides of the mirror, and they are on the same side of the principal axis. Consider all the cases of images formed in spherical mirrors and carefully determine the incorrect option.


Complete answer:
Option A
For spherical mirrors, let us first consider the case of O and I being on the same side of the principal axis.
We know that virtual images are the ones which are formed on the same side of the principal axis as that of the object. We also know that a virtual image is formed behind the mirror, that is, the object and the virtual image of the object are on the opposite sides of the mirror.
Hence, if O and I are on the same side of the principal axis, then they’ll be on the opposite sides of the mirror.
Option B
Now, let us consider the second case of O and I being on the opposite sides of the principal axis.
We know that real images are the ones which are formed on the opposite side of the principal axis as that of the object. We also know that a real image is formed on the same side of the mirror as that of the object.
Hence, if O and I are on the opposite sides of the principal axis, then they’ll be on the same side of the mirror.
Option D
Now, let us consider the third case of O being on the principal axis.
In this case, the object is lying at the normal of the mirror, therefore, the image will also be formed on the principal axis.
Considering all the three cases, we observed that option C is the incorrect one because real images which lie on the opposite side of the principal axis always lie on the same side of the mirror where the object is placed .
Hence, the incorrect option is C.

Note: Basic knowledge of all the cases of images formed by spherical mirrors is a must to solve the above question. Keep in mind how real images are formed and how virtual images are formed and what are their locations with respect to the object.