Question: I is the image of a point object O formed by spherical mirror, then which of the following statement...

Question

I is the image of a point object O formed by spherical mirror, then which of the following statements is incorrect:

Answer 1

Solution

The question asks us to identify the incorrect statement regarding the image (I) of a point object (O) formed by a spherical mirror. We will analyze each statement based on the properties of image formation by spherical mirrors.

Key Concepts:

Real Image: Formed by actual intersection of reflected rays. Always formed on the same side of the mirror as the real object. For a real object, real images are always inverted.
Virtual Image: Formed when reflected rays appear to diverge from a point. Always formed on the opposite side of the mirror from the real object. For a real object, virtual images are always erect.
Erect Image: Object and image are on the same side of the principal axis (e.g., both above or both below).
Inverted Image: Object and image are on opposite sides of the principal axis (e.g., one above, one below).
Principal Axis: The line passing through the pole (P) and the center of curvature (C) of the mirror.

Assumption: Unless specified otherwise, "point object O" is generally considered a real object. We will proceed with this assumption first.

Let's analyze each statement:

(A) If O and I are on same side of the principal axis, then they have to be on opposite sides of the mirror.

"O and I are on same side of the principal axis" means the image is erect with respect to the object.
For a real object, an erect image formed by a spherical mirror is always virtual.
A virtual image is always formed on the opposite side of the mirror from the real object.
Conclusion: This statement is correct. (e.g., concave mirror with object between P and F; convex mirror with any real object).

(B) If O and I are on opposite side of the principal axis, then they have to be on same side of the mirror.

"O and I are on opposite side of the principal axis" means the image is inverted with respect to the object.
For a real object, an inverted image formed by a spherical mirror is always real.
A real image is always formed on the same side of the mirror as the real object.
Conclusion: This statement is correct. (e.g., concave mirror with object beyond F).

(C) If O and I are on opposite side of the principal axis, then they can be on opposite side of the mirror as well.

"O and I are on opposite side of the principal axis" implies the image is inverted.
As established in (B), for a real object, an inverted image is always real.
A real image is always formed on the same side of the mirror as the real object.
Therefore, it is impossible for an inverted image (O and I on opposite sides of principal axis) to be formed on the opposite side of the mirror if O is a real object.
Conclusion (assuming real object): This statement is incorrect.

(D) If O is on principal axis then I has to lie on principal axis only.

This is a fundamental property of optical systems with axial symmetry (like spherical mirrors). If a point object is placed on the principal axis, its image will also be formed on the principal axis. This is due to the symmetry of the mirror about the principal axis. Any ray originating from a point on the principal axis and reflecting off the mirror will intersect the principal axis at the image point.
Conclusion: This statement is correct.

Final Check: Based on the common interpretation that "point object O" refers to a real object, statement (C) is the incorrect one.

If we consider the possibility of a virtual object: A virtual object for a concave mirror, if placed between P and F (behind the mirror), forms a real, inverted image in front of the mirror. In this specific case, O (virtual) is behind the mirror, I (real) is in front of the mirror, so they are on opposite sides of the mirror. Also, O and I are on opposite sides of the principal axis (inverted image). This scenario would make statement (C) correct.

However, in the context of general questions in competitive exams, "object" implies a real object unless explicitly stated as "virtual object". If the question intended to include virtual objects, it should have been specified or the options should be structured to reflect this complexity. Given the options, the most straightforward and common interpretation leads to (C) being incorrect.

The question asks for the incorrect statement. Under the standard assumption of a real object, statement (C) is definitively incorrect.